WebSVN – svnkaklik – Path Comparison – / – /dokumenty Rev 620 and /dokumenty/ Rev 660

Ignore whitespace Rev 620 → Rev 660

 /dokumenty/PRA1/11-Rotace/Rotace.tex
 ,9 → 16,17
 \begin{abstract}
 \end{abstract}
-\section{Úvod}
+\section{Pracovní Úkoly}
 \begin{enumerate}
 \item V domácí přípravě odvoďte vzorec pro výpočet momentu setrvačnosti válce a dutého válce.
+\begin{equation}
+I = \frac{1}{2} MR^2
+\end{equation}
+\begin{equation}
+I = \frac{1}{2} M(R_1^2 + R_2^2)
+\end{equation}
 \item Změřte momenty setrvačnosti přiložených rotačních objektů experimentálně a porovnejte je s hodnotami z teoretických vzorců. Měření proveďte alespoň pětkrát. Použijte disk, disk + prstenec a pomocí nich stanovte moment setrvačnosti samotného prstence.
 \item Změřte moment setrvačnosti disku, umístěného na dráze mimo osu rotace a pomocí výsledků z předchozího úkolu ověřte platnost Steinerovy věty.
 \item Ověřte zákon zachování momentu hybnosti. Do protokolu přiložte graf závislosti úhlové rychlosti rotace na čase.
 ,6 → 52,13
 \includegraphics[width=150mm]{./data/rotace_zmena.pdf}
+Proložením dat jsme spočítali momenty setrvačnosti disku $(9.63 \pm 0,05) 10^{-3} kgm^2$ dále moment setrvačnosti prstence $(5.11 \pm 0,01) 10^{-3} kgm^2$.  úkolem také bylo ověřit platnost Steinerovy věty, k tomu jsme stejným způsobem museli nejdříve změřit moment setrvačnosti držáku $(12.81 \pm 0,02) 10^{-3} kgm^2$ a následně celého systému s prstencem posunutým o 50mm od osy rotace. V takovém případě byl moment setrvačnosti $(10.31 \pm 0,06) 10^{-3} kgm^2$
+\subsection{Zachování momentu hybnosti}
+Při tomto úkolu jsme na držák přidali dvě závaží tak aby je bylo možné je během rotace šňůrkou stáhnout k sobě.
+Tím se změnila úhlová rychlost z 2,5 rad/s na 9,2 rad/s při změně momentu setrvačnosti z 0.0254 $kgm^2$ na 0.0073 $kgm^2$ aby moment hybnosti zůstal zachován s chybou 5\%.
 \subsection{Precese gyroskopu}
 Precesi gyroskopu jsme měřili tak že v jsme jej v klidu vyvážili a na straně s gyroskopem zatížili definovaným závažím o hmotnosti 17,9 g. Které působí na gyroskop tíhovou silou. Která způsobuje precesi gyroskopu kolem svislé osy.
 ,10 → 77,10
 \end{table}
 \section{Diskuse}
-Největším problémem bylo měření zachování momentu hybnosti, kdy aparatura přecházela při změně konfirugace závaží do neopakovatelně definovaných stavů, což pravděpodobně  způsobilo značnou chybu.
+Největším problémem bylo měření zachování momentu hybnosti, kdy aparatura přecházela při změně konfigurace závaží do neopakovatelně definovaných stavů, což pravděpodobně způsobilo značnou chybu.
 \section{Závěr}
-Z naměřených dat lze potvrdit že momenty setrvačností objektů rotujících na téže ose se sčítají.
+Z naměřených dat lze potvrdit že momenty setrvačností objektů rotujících na téže ose se sčítají. A moment hybnosti se při změně momentu setrvačnosti zachovává. Průměrná hodnota precese gyroskopu nám vyšla 0,0176 rad/s.
 \begin{thebibliography}{99}
 \bibitem{oscilace}{Zadání úlohy 11 - Dynamika rotačního pohybu}. \href{http://praktika.fjfi.cvut.cz/RotacniPohyb/}{http://praktika.fjfi.cvut.cz/RotacniPohyb/}.

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 /dokumenty/PRA1/12-Tepelne_stroje/Tepelne_stroje.tex
 ,21 → 14,36
 \maketitle
 \thispagestyle{empty}
 \begin{abstract}
+Zabývali jsme se schopností tepelného stroje přeměňovat teplo na práci. Pracovní plyn tepelného stroje po zahřátí zdvihal závaží, čímž konal mechanickou práci. Práci konanou plynem jsme měřili tlakovým a rotačním senzorem.
+\end{abstract}
-\end{abstract}
-\section{Úvod}
+\section{Pracovní úkoly}
 \begin{enumerate}
 \item Zkalibrujte tlakoměr, zkontrolujte čidlo pro odečítání polohy pístu.
 \item rozeberte nastíněný pracovní cyklus, popište jeho jednotlivé fáze v p - V diagramu.
-\item Proveďte opakovaně popsaný cyklus s různými závažími. Získejte pro každé měření plochu uzavřenou křivkami v p-V diagramu a spočítejte rozdíl potenciálních energií pro dané závaží. Vynášejte obě hodnoty do grafu, výsledné hodnoty proložte přímkou. $W =a* \Delta E+b$
+\item Proveďte opakovaně popsaný cyklus s různými závažími. Získejte pro každé měření plochu uzavřenou křivkami v p-V diagramu a spočítejte rozdíl potenciálních energií pro dané závaží. Vynášejte obě hodnoty do grafu, výsledné hodnoty proložte přímkou. $W =a \cdot \Delta E+b$
+\item Změřte hodnotu vnitřního odporu Peltierovy součástky.
+\item Změřte účinnost Peltierova aparátu. Srovnejte s účinností Carnotova cyklu pro lázně stejných teplot. Opakujte několik měření pro různé teploty horké lázně. Vyneste hodnoty \begin{math}\varepsilon_{carnot},\,\varepsilon \end{math} do grafu, kde na ose x bude teplota horké lázně.
+\item Započítejte k účinnosti vnitřní odpor a výkon obcházející součástku. K energii rozptýlené na zátěžovém odporu je třeba přidat energii rozptýlenou na vnitřním odporu.
 \end{enumerate}
+\section{Úvod}
+Tepelný stroj je užitečné zařízení oblíbené hlavně kvůli svojí schopnosti převádět část tepelné energie na užitečnou práci. Účinnost takového stoje je dána vztahem.
+\begin{equation}
+ W = Q_1 - Q_2 = Q_1\frac{T_1 - T_2}{T_1}, \label{carnot}
+\end{equation}čímž je dána maximální teoretická účinnost tepelného stroje
+\begin{equation}
+ \varepsilon_{max} = \frac{T_1 - T_2}{T_1} \label{ucinnost}
+\end{equation}
+V reálné situaci je tato účinnost menší z důvodu působení disipativních sil na různé části stroje, které způsobí, že část mechanické energie je přeměněna zpět na nepoužitelné teplo.
 \section{Postup měření}
 \subsection{Měření účinnosti Peltierova článku}
-Aparaturu jsme zapojili podle zadání tak, aby bylo možné meřit elektricky přikon do zahřívacího odporu i výkon dodávaný do zátěže  Peltierovým článkem.
+Aparaturu jsme zapojili podle zadání tak, aby bylo možné měřit elektrický příkon do zahřívacího odporu i výkon dodávaný do zátěže  Peltierovým článkem.
-Po uvedení přístrojů do provozu měření probýhalo, tak, že jsme nastavili teplotu horké lázně a při odpojené zátěži počkali, až se ustálí. Následně jsme odečetli napětí, na Peltierově článku. A zátěž zapojili, teplotu horké lázně bylo nyní potřeba dorovnat na teplotu při odpojené zátěži, aby bylo možné určit vnitřní odpor měřeného článku a tepelný výkon, který neprochází přímo aktivní oblastí. Naměřená data jsou uvedena v tabulce \ref{Peltier} kde každý druhý řádek odpovídá připojené zátěži R = 2 Ohm.
+Po uvedení přístrojů do provozu měření probíhalo tak, že jsme nastavili teplotu horké lázně a při odpojené zátěži počkali, až se ustálí. Následně jsme odečetli napětí, na Peltierově článku. A zátěž zapojili, teplotu horké lázně bylo nyní potřeba dorovnat na teplotu při odpojené zátěži, aby bylo možné určit vnitřní odpor měřeného článku a tepelný výkon, který neprochází přímo aktivní oblastí. Naměřená data jsou uvedena v tabulce \ref{Peltier} kde každý druhý řádek odpovídá připojené zátěži R = 2 Ohm.
 \begin{table}[htbp]
 \begin{center}
 ,25 → 66,35
 \label{Peltier}
 \end{table}
-Z těchto hodnot jsme pak vypočetli jeho účinnost, která byla bez korekce pod jedním procentem. Jak je vidět na grafu \ref{PeltierXCarnot}.
+Z těchto hodnot jsme pak podle zdroje \cite{Peltier} vypočetli jeho účinnost, která byla bez korekce pod jedním procentem. Jak je vidět na grafu \ref{PeltierXCarnot}. Hodnota vnitřního elektrického odporu Peltierovy součástky nám vyšla 1,34 $m\Omega$.
 \begin{figure}
 \begin{center}
 \includegraphics[width=150mm]{peltier.pdf}
 \end{center}
+\caption{Učinnost Peltierova článku v porovnání s ideálním Carnotovým strojem za stejných podmínek}
 \label{PeltierXCarnot}
-\caption{Učinnost Peltierova článku v porovnání s Carnotovým strojem za stejných podmínek}
 \end{figure}
-Při aplikování korekce na vnitřní odpor a tepelné ztráty se účinnost dostala přibližně ke 4,55\%,
+Při aplikování korekce na vnitřní odpor a tepelné ztráty (opět podle zdroje \cite{Peltier}) se účinnost dostala přibližně na 4,55\%.
 \subsection{Carnotův Cyklus}
-Tepelný stroj jsme zatěžovali závažím o definované hmotnosti a ze změny jeho potenciální energie jsme určili práci, kterou stoj vykonal.
-Energii v Carnotova cyklu jsme získali výpočtem z uzavřené plochy p-V diagramu. Náš naměřený výsledek je vidět v grafu \ref{carnot}.
+Po kalibraci tlakoměru závažím hmotnosti (100g)
+Jsme píst tepelného stroje zatěžovali závažím o definované hmotnosti a ze změny jeho potenciální energie v průběhu pracovního cyklu viz. obrázek \ref{cyklus} jsme určili práci, kterou stroj vykonal.
+Energii v Carnotova cyklu jsme získali výpočtem z uzavřené plochy p-V diagramu V programu DataStudio. Náš naměřený výsledek je vidět v grafu \ref{carnot}.
 \begin{figure}
 \begin{center}
+\includegraphics[width=150mm]{./data/tepl100g.png}
+\end{center}
+\caption{Pracovní cyklus pístu zatíženého závažím 100g}
+\label{cyklus}
+\end{figure}
+\begin{figure}
+\begin{center}
 \includegraphics[width=150mm]{carnot.pdf}
 \caption{Práce a energie laboratorního tepelného stroje.}
 \label{carnot}
 ,7 → 101,7
 \end{center}
 \end{figure}
-Při nafitování naměřených bodů výrazem $W =a* \Delta E+b$ se ukázalo, že koeficienty jsou: $a = 1.04815 \pm 0.01257$ , $b = 0.00517276 \pm 0.0008125$ Což znamená, že účinnost laboratorní aparatury je přibližně 95\%.
+Při nafitování naměřených bodů výrazem $W =a \cdot \Delta E+b$ se ukázalo, že koeficienty jsou: $a = 1.04815 \pm 0.01257$ , $b = 0.00517276 \pm 0.0008125$ Což znamená, že mechanická účinnost laboratorní aparatury je přibližně 95\%. Což není překvapivé vzhledem k jednoduchosti stroje, kdy je navíc pracovní medium přemisťováno mezi chladnou a studenou lázní za pomoci jiného zdroje energie.
 \section{Diskuse}
 Při měření Peltierova článku by bylo asi vhodné použít kratší přívodní hadičky ke chladící lázni, jelikož voda se tak zbytečně ohřívá z původní teploty tání ledu a teplota studené strany článku se tak stává nestabilní.
 ,6 → 112,6
 \begin{thebibliography}{99}
 \bibitem{Stroje}{Zadání úlohy 12 - Tepelný stroj}. \href{http://praktika.fjfi.cvut.cz/TepelnyStroj}{http://praktika.fjfi.cvut.cz/TepelnyStroj}
-\bibitem{Stroje}{Zadání úlohy 12 -   Účinnost tepelného stroje}.\href{http://fyzika.fjfi.cvut.cz/Peltier}{http://fyzika.fjfi.cvut.cz/Peltier}
+\bibitem{Peltier}{Zadání úlohy 12 -  Účinnost tepelného stroje}.\href{http://fyzika.fjfi.cvut.cz/Peltier}{http://fyzika.fjfi.cvut.cz/Peltier}
 \end{thebibliography}
 \end{document}

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 %%BeginFont: CMSY10
 %!PS-AdobeFont-1.1: CMSY10 1.0
 %%CreationDate: 1991 Aug 15 07:20:57
 ,6 → 484,7
 /Encoding 256 array
 1 255 {1 index exch /.notdef put} for
 dup 0 /minus put
+dup 6 /plusminus put
 readonly def
 /FontBBox{-29 -960 1116 775}readonly def
 currentdict end
 ,14 → 500,18
 DE3302B2E6B819CB6AE455B1AF3187FFE8071AA57EF8A6616B9CB7941D44EC7A
 A7BB3DF755178D7D2E4BB69859EFA4BBC30BD6BB1531133FD4D9438FF99F09
 ECC068A324D75B5F696B8688EEB2F17E5ED34CCD6D047A4E3806D000C199D7C
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 ,6 → 762,7
 dup 73 /I put
 dup 80 /P put
 dup 86 /V put
+dup 99 /c put
 readonly def
 /FontBBox{-24 -250 1110 750}readonly def
 currentdict end
 ,36 → 791,40
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 0000000000000000000000000000000000000000000000000000000000000000
 0000000000000000000000000000000000000000000000000000000000000000
 ,12 → 859,15
 dup 58 /period put
 dup 59 /comma put
 dup 60 /less put
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 dup 67 /C put
 dup 84 /T put
 dup 86 /V put
 dup 98 /b put
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 dup 103 /g put
 dup 104 /h put
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 dup 107 /k put
 dup 108 /l put
 dup 109 /m put
 ,129 → 918,142
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 cleartomark
 %%EndFont
-%%BeginFont: CMBX12
-%!PS-AdobeFont-1.1: CMBX12 1.0
-%%CreationDate: 1991 Aug 20 16:34:54
-% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
-dict begin
-/FontInfo 7 dict dup begin
-/version (1.0) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMBX12) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Bold) readonly def
-/ItalicAngle 0 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMBX12 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-1 255 {1 index exch /.notdef put} for
-dup 16 /dotlessi put
-dup 19 /acute put
-dup 20 /caron put
-dup 46 /period put
-dup 49 /one put
-dup 50 /two put
-dup 51 /three put
-dup 52 /four put
-dup 53 /five put
-dup 68 /D put
-dup 77 /M put
-dup 80 /P put
-dup 82 /R put
-dup 85 /U put
-dup 90 /Z put
-dup 97 /a put
-dup 99 /c put
-dup 100 /d put
-dup 101 /e put
-dup 102 /f put
-dup 104 /h put
-dup 105 /i put
-dup 107 /k put
-dup 108 /l put
-dup 109 /m put
-dup 110 /n put
-dup 111 /o put
-dup 112 /p put
-dup 114 /r put
-dup 115 /s put
-dup 116 /t put
-dup 117 /u put
-dup 118 /v put
-dup 122 /z put
-readonly def
-/FontBBox{-53 -251 1139 750}readonly def
-currentdict end
-currentfile eexec
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 %%CreationDate: 1991 Aug 20 16:38:05
 ,6 → 1085,7
 /Encoding 256 array
 1 255 {1 index exch /.notdef put} for
 dup 12 /fi put
+dup 13 /fl put
 dup 16 /dotlessi put
 dup 19 /acute put
 dup 20 /caron put
 ,6 → 1118,7
 dup 72 /H put
 dup 74 /J put
 dup 75 /K put
+dup 76 /L put
 dup 77 /M put
 dup 78 /N put
 dup 79 /O put
 ,324 → 1182,334
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+1954 a Black
+2086 a Fh(1.)p Black 49 w(Zm)m(\024)-46 b(e)-5 b(\024)-43
+b(rte)32 b(k)m(ompres)-11 b(\023)-38 b(\020)34 b(plyn)m(u)g(ob)5
+b(jem)34 b(ba)s(\024)-51 b(nky)32 b(syst)m(\023)-46 b(em)m(u)35
+b(s)e(kmita)5 b(j)-11 b(\023)-38 b(\020c)-11 b(\023)-38
+b(\020m)34 b(p)-11 b(\023)-38 b(\020stk)m(em.)0 2146
+y
 SDict begin H.S end
-2174 a
-2174 a
+2146 a 0 2146 a
 SDict begin 14.5 H.A end
-2174 a 0 2174 a
+2146 a 0 2146 a
 SDict begin [ /View [/XYZ H.V] /Dest (Item.2) cvn H.B /DEST pdfmark end
-2174 a Black 119 2317 a
-Fh(2.)p Black 49 w(Zm)m(\024)-46 b(e)-5 b(\024)-43 b(rte)44
-b(P)m(oissono)m(vu)j(k)m(onstan)m(tu)g(meto)s(dou)e(adiabatic)m(k)m
-(\023)-46 b(e)46 b(expanze)g(a)f(sou)m(\024)-46 b(casn)m(\024)g(e)46
-b(meto)s(dou)244 2437 y(kmita)5 b(j)-11 b(\023)-38 b(\020c)-11
-b(\023)-38 b(\020ho)34 b(p)-11 b(\023)-38 b(\020stku.)0
-y
+2146 a Black
+2286 a Fh(2.)p Black 49 w(Zm)m(\024)-46 b(e)-5 b(\024)-43
+b(rte)44 b(P)m(oissono)m(vu)j(k)m(onstan)m(tu)g(meto)s(dou)e(adiabatic)
+m(k)m(\023)-46 b(e)46 b(expanze)g(a)f(sou)m(\024)-46
+b(casn)m(\024)g(e)46 b(meto)s(dou)244 2407 y(kmita)5
+b(j)-11 b(\023)-38 b(\020c)-11 b(\023)-38 b(\020ho)34
+b(p)-11 b(\023)-38 b(\020stku.)0 2466 y
 SDict begin H.S end
-2498 a 0 2498 a
+2466 a 0 2466
+a
 SDict begin 14.5 H.A end
-2498 a 0 2498 a
+2466 a 0 2466 a
 SDict begin [ /View [/XYZ H.V] /Dest (Item.3) cvn H.B /DEST pdfmark end
-2498 a Black
-2641 a Fh(3.)p Black 49 w(Oba)43 b(v)q(\023)-50 b(ysledky)47
-b(p)s(oro)m(vnejte.)d(V)q(\023)-50 b(ysledek)46 b(meto)s(dy)e(kmita)5
-b(j)-11 b(\023)-38 b(\020c)-11 b(\023)-38 b(\020ho)45
-b(p)-11 b(\023)-38 b(\020stku)45 b(p)s(o)m(v)-5 b(a)m(\024)-46
-b(zujte)44 b(za)f(tab-)244 2761 y(ulk)m(o)m(v)m(ou)34
+2466 a Black 119 2607 a Fh(3.)p
+Black 49 w(Oba)43 b(v)q(\023)-50 b(ysledky)47 b(p)s(oro)m(vnejte.)d(V)q
+(\023)-50 b(ysledek)46 b(meto)s(dy)e(kmita)5 b(j)-11
+b(\023)-38 b(\020c)-11 b(\023)-38 b(\020ho)45 b(p)-11
+b(\023)-38 b(\020stku)45 b(p)s(o)m(v)-5 b(a)m(\024)-46
+b(zujte)44 b(za)f(tab-)244 2727 y(ulk)m(o)m(v)m(ou)34
 b(ho)s(dnotu)f(P)m(oissono)m(vy)i(k)m(onstan)m(t)m(y)-8
-b(.)0 2930 y
+b(.)0 2787 y
 SDict begin H.S end
-2930 a 0 2930 a
+2787 a 0 2787 a
 SDict begin 14.5 H.A end
-2930 a 0 2930 a
-SDict begin [ /View [/XYZ H.V] /Dest (section.2) cvn H.B /DEST pdfmark end
-2930
-a 164 x Fi(2)264 3059 y(\023)242 3094 y(Uv)l(o)t(d)0
-y
+2787 a 0 2787 a
+SDict begin [ /View [/XYZ H.V] /Dest (Item.4) cvn H.B /DEST pdfmark end
+2787
+a Black 119 2928 a Fh(4.)p Black 49 w(Jednolitro)m(v)m(ou)34
+b(l\023)-49 b(ahev)33 b(zv)-5 b(a)m(\024)-46 b(zte)34
+b(pr\023)-49 b(azdnou.)0 2987 y
 SDict begin H.S end
-3192 a 0 3192 a
+2987 a 0 2987 a
 SDict begin 14.5 H.A end
-3192 a 0 3192 a
-SDict begin [ /View [/XYZ H.V] /Dest (subsection.2.1) cvn H.B /DEST pdfmark end
-3192 a 150
-x Fg(2.1)135 b(Mo)t(dul)45 b(pru)l(\024)-64 b(znosti)45
-b(v)g(tah)l(u)0 3527 y Fh(P)m(oissono)m(v)-5 b(a)39 b(k)m(onstan)m(ta)f
-Ff(\024)g Fh(je)f(p)s(om)m(\024)-46 b(er)38 b(m)m(\024)-46
-b(ern)m(\023)g(eho)39 b(tepla)e Ff(C)2179 3542 y Fe(P)2275
-y Fh(p)-5 b(\024)-43 b(ri)37 b(st\023)-49 b(al)m(\023)j(em)38
-b(tlaku)g(k)m(e)g(m)m(\024)-46 b(ern)m(\023)g(em)m(u)40
-b(teplu)0 3647 y Ff(C)70 3662 y Fe(V)163 3647 y Fh(p)-5
-b(\024)-43 b(ri)32 b(st\023)-49 b(al)m(\023)j(em)33 b(ob)5
-b(jem)m(u)1707 3810 y Ff(\024)28 b Fh(=)1906 3743 y Ff(C)1976
-y Fe(P)p 1905 3787 131 4 v 1905 3878 a Ff(C)1975
-y Fe(V)2045 3810 y Ff(:)146 4025 y(\024)49 b Fh(m\023)-49
-b(a)48 b(v)m(e)i(v)-5 b(\024)-44 b(sec)m(h)50 b(sousta)m(v\023)-49
-b(ac)m(h)51 b(stejnou)46 b(\024)-46 b(c)-11 b(\023)-38
-b(\020selnou)50 b(ho)s(dnotu.)f(Pro)f(v)-5 b(\024)-44
-b(sec)m(hn)m(y)52 b(plyn)m(y)e(je)e(p)s(om)m(\024)-46
-b(er)0 4145 y(sp)s(eci\014c)m(k)q(\023)c(yc)m(h)44 b(tep)s(el)d
-Ff(\024)f Fh(v)m(\024)-46 b(et)-5 b(\024)-44 b(s)-11
-b(\023)-38 b(\020)41 b(ne)m(\024)-46 b(z)41 b(1)f(a)g(z\023)-49
-b(avis)-11 b(\023)-38 b(\020)41 b(na)f(p)s(o)m(\024)-46
-b(ctu)40 b(atom)-9 b(\027)-64 b(u)41 b(v)f(molekule)i(plyn)m(u.)f(Ho)s
-(dnotu)f Ff(\024)0 4266 y Fh(m)-9 b(\027)-64 b(u)m(\024)-46
-b(zeme)34 b(ur)m(\024)-46 b(cit)33 b(ze)g(zm)m(\024)-46
-b(en)m(y)35 b(tlaku)e(p)-5 b(\024)-43 b(ri)31 b(adiabatic)m(k)m(\023)
--46 b(em)35 b(d)m(\024)-46 b(eji,)33 b(kter)q(\023)-50
-b(y)33 b(je)g(p)s(ops\023)-49 b(an)33 b(P)m(oissono)m(v)m(ou)h(ro)m
-(vnic)-11 b(\023)-38 b(\020)1604 4505 y Ff(pV)1732 4464
-y Fe(\024)1804 4505 y Fh(=)28 b Ff(k)s(onst:)146 4725
-y Fh(kde)34 b Ff(p)p Fh(,)e Ff(V)55 b Fh(jsou)32 b(tlak)h(a)f(ob)5
-b(jem)34 b(plyn)m(u.)146 4845 y(Pro)22 b(m)m(\024)-46
-b(e)-5 b(\024)-43 b(ren)-11 b(\023)-38 b(\020)22 b(P)m(oissono)m(vy)i
-(k)m(onstan)m(t)m(y)g(vzduc)m(h)m(u)g(jsme)f(mimo)f(jin)m(\023)-46
-b(e)22 b(p)s(ou)m(\024)-46 b(zili)22 b(Cl)m(\023)-46
-b(emen)m(to)m(vu-D)m(\023)g(esormeso)m(vu)0 4966 y(meto)s(du.)36
-b(Jej)-11 b(\023)-38 b(\020)m(\024)-46 b(z)36 b(princip)g(sp)s(o)m
-(\024)-46 b(c)-11 b(\023)-38 b(\020v\023)-49 b(a)36 b(v)m(e)g(stla)m
-(\024)-46 b(cen)-11 b(\023)-38 b(\020)37 b(vzduc)m(h)m(u)g(v)m(e)g(v)m
-(elk)m(\023)-46 b(e)37 b(b\023)-49 b(ani,)35 b(ab)m(y)h(m)m(\024)-46
+2987
+a 0 2987 a
+SDict begin [ /View [/XYZ H.V] /Dest (Item.5) cvn H.B /DEST pdfmark end
+2987 a Black 119 3128 a Fh(5.)p Black 49
+w(Jednolitro)m(v)m(ou)34 b(l\023)-49 b(ahev)33 b(zv)-5
+b(a)m(\024)-46 b(zte)34 b(plnou)f(v)m(o)s(dy)-8 b(.)0
+y
+SDict begin H.S end
+3187 a 0 3187 a
+SDict begin 14.5 H.A end
+3187 a 0 3187 a
+SDict begin [ /View [/XYZ H.V] /Dest (Item.6) cvn H.B /DEST pdfmark end
+3187 a Black
+3328 a Fh(6.)p Black 49 w(Z)32 b(ob)s(ou)g(v)q(\023)-50
+b(ysledk)-9 b(\027)-64 b(u)35 b(ur)m(\024)-46 b(cete)34
+b(ob)5 b(jem)33 b(lah)m(v)m(e.)0 3387 y
+SDict begin H.S end
+3387 a 0 3387
+a
+SDict begin 14.5 H.A end
+3387 a 0 3387 a
+SDict begin [ /View [/XYZ H.V] /Dest (Item.7) cvn H.B /DEST pdfmark end
+3387 a Black 119 3528 a Fh(7.)p
+Black 49 w(Ob)5 b(jem)33 b(pr\023)-49 b(azdn)m(\023)j(e)34
+b(jednotlitro)m(v)m(\023)-46 b(e)34 b(lah)m(v)m(e)g(ur)m(\024)-46
+b(cete)33 b(k)m(ompres)-11 b(\023)-38 b(\020)35 b(plyn)m(u.)0
+y
+SDict begin H.S end
+3588 a 0 3588 a
+SDict begin 14.5 H.A end
+3588 a 0 3588 a
+SDict begin [ /View [/XYZ H.V] /Dest (Item.8) cvn H.B /DEST pdfmark end
+3588 a Black
+3729 a Fh(8.)p Black 49 w(Stejn)q(\023)-50 b(ym)41
+b(p)s(ostup)s(em)g(zm)m(\024)-46 b(e)-5 b(\024)-43 b(rte)40
+b(ob)5 b(jem)41 b(hadi)m(\024)-46 b(cky)42 b(sp)s(o)5
+b(juj)-11 b(\023)-38 b(\020c)-11 b(\023)-38 b(\020)41
+b(b)m(yretu)g(s)g(m)m(\024)-46 b(e)-5 b(\024)-43 b(ren)q(\023)-50
+b(ym)41 b(prostorem.)244 3849 y(T)-8 b(uto)33 b(ho)s(dnotu)f(o)s(de)m
+(\024)-46 b(ct)m(\024)g(ete)34 b(o)s(d)e(v)q(\023)-50
+b(ysledku)35 b(p)s(o)s(dle)e(b)s(o)s(du)f(4.)0 4017 y
+SDict begin H.S end
+4017 a 0 4017 a
+SDict begin 14.5 H.A end
+4017 a 0 4017 a
+SDict begin [ /View [/XYZ H.V] /Dest (section.2) cvn H.B /DEST pdfmark end
+4017 a 163 x Fi(2)264
+y(\023)242 4180 y(Uv)l(o)t(d)0 4399 y Fh(P)m(oissono)m(v)-5
+b(a)39 b(k)m(onstan)m(ta)f Fg(\024)g Fh(je)f(p)s(om)m(\024)-46
+b(er)38 b(m)m(\024)-46 b(ern)m(\023)g(eho)39 b(tepla)e
+Fg(C)2179 4414 y Ff(P)2275 4399 y Fh(p)-5 b(\024)-43
+b(ri)37 b(st\023)-49 b(al)m(\023)j(em)38 b(tlaku)g(k)m(e)g(m)m(\024)-46
+b(ern)m(\023)g(em)m(u)40 b(teplu)0 4519 y Fg(C)70 4534
+y Ff(V)163 4519 y Fh(p)-5 b(\024)-43 b(ri)32 b(st\023)-49
+b(al)m(\023)j(em)33 b(ob)5 b(jem)m(u)1707 4683 y Fg(\024)28
+b Fh(=)1906 4615 y Fg(C)1976 4630 y Ff(P)p 1905 4659
+4 v 1905 4751 a Fg(C)1975 4766 y Ff(V)2045 4683 y
+Fg(:)146 4893 y(\024)49 b Fh(m\023)-49 b(a)48 b(v)m(e)i(v)-5
+b(\024)-44 b(sec)m(h)50 b(sousta)m(v\023)-49 b(ac)m(h)51
+b(stejnou)46 b(\024)-46 b(c)-11 b(\023)-38 b(\020selnou)50
+b(ho)s(dnotu.)f(Pro)f(v)-5 b(\024)-44 b(sec)m(hn)m(y)52
+b(plyn)m(y)e(je)e(p)s(om)m(\024)-46 b(er)0 5013 y(sp)s(eci\014c)m(k)q
+(\023)c(yc)m(h)44 b(tep)s(el)d Fg(\024)f Fh(v)m(\024)-46
+b(et)-5 b(\024)-44 b(s)-11 b(\023)-38 b(\020)41 b(ne)m(\024)-46
+b(z)41 b(1)f(a)g(z\023)-49 b(avis)-11 b(\023)-38 b(\020)41
+b(na)f(p)s(o)m(\024)-46 b(ctu)40 b(atom)-9 b(\027)-64
+b(u)41 b(v)f(molekule)i(plyn)m(u.)f(Ho)s(dnotu)f Fg(\024)0
+y Fh(m)-9 b(\027)-64 b(u)m(\024)-46 b(zeme)34 b(ur)m(\024)-46
+b(cit)33 b(ze)g(zm)m(\024)-46 b(en)m(y)35 b(tlaku)e(p)-5
+b(\024)-43 b(ri)31 b(adiabatic)m(k)m(\023)-46 b(em)35
+b(d)m(\024)-46 b(eji,)33 b(kter)q(\023)-50 b(y)33 b(je)g(p)s(ops\023)
+-49 b(an)33 b(P)m(oissono)m(v)m(ou)h(ro)m(vnic)-11 b(\023)-38
+b(\020)1604 5362 y Fg(pV)1732 5320 y Ff(\024)1804 5362
+y Fh(=)28 b Fg(k)s(onst:)146 5570 y Fh(kde)34 b Fg(p)p
+Fh(,)e Fg(V)55 b Fh(jsou)32 b(tlak)h(a)f(ob)5 b(jem)34
+b(plyn)m(u.)146 5691 y(Pro)22 b(m)m(\024)-46 b(e)-5 b(\024)-43
+b(ren)-11 b(\023)-38 b(\020)22 b(P)m(oissono)m(vy)i(k)m(onstan)m(t)m(y)
+g(vzduc)m(h)m(u)g(jsme)f(mimo)f(jin)m(\023)-46 b(e)22
+b(p)s(ou)m(\024)-46 b(zili)22 b(Cl)m(\023)-46 b(emen)m(to)m(vu-D)m
+(\023)g(esormeso)m(vu)0 5811 y(meto)s(du.)36 b(Jej)-11
+b(\023)-38 b(\020)m(\024)-46 b(z)36 b(princip)g(sp)s(o)m(\024)-46
+b(c)-11 b(\023)-38 b(\020v\023)-49 b(a)36 b(v)m(e)g(stla)m(\024)-46
+b(cen)-11 b(\023)-38 b(\020)37 b(vzduc)m(h)m(u)g(v)m(e)g(v)m(elk)m
+(\023)-46 b(e)37 b(b\023)-49 b(ani,)35 b(ab)m(y)h(m)m(\024)-46
 b(el)36 b(proti)f(vn)m(\024)-46 b(ej)-5 b(\024)-44 b(s)-11
-b(\023)-38 b(\020m)m(u)0 5086 y(barometric)m(k)m(\023)-46
-b(em)m(u)40 b(tlaku)d Ff(b)h Fh(p)-5 b(\024)-43 b(retlak)37
-b Ff(h)p Fh(.)g(T)-8 b(en)38 b(o)s(de)m(\024)-46 b(cteme)38
-b(jak)m(o)g(v)q(\023)-50 b(y)-5 b(\024)-44 b(sk)m(o)m(v)q(\023)-50
-b(y)40 b(rozd)-11 b(\023)-38 b(\020l)38 b(hladin)f(otev)-5
-b(\024)-43 b(ren)m(\023)d(eho)0 5207 y(manometru,)33
-b(kter)q(\023)-50 b(y)34 b(je)f(k)g(b\023)-49 b(ani)33
-b(p)-5 b(\024)-43 b(rip)s(o)5 b(jen.)32 b(Tlak)h(vzduc)m(h)m(u)i(v)e
-(b\023)-49 b(ani)33 b(je)g(pak)1658 5427 y Ff(p)1707
-y Fd(1)1774 5427 y Fh(=)27 b Ff(b)c Fh(+)f Ff(h:)146
-y Fh(P)-5 b(\024)-43 b(r)-11 b(\023)-38 b(\020slu)-5
-b(\024)-44 b(sn)q(\023)-50 b(y)33 b(ob)5 b(jem)32 b(vzduc)m(h)m(u)i(p)
--5 b(\024)-43 b(red)31 b(adiabatic)m(k)m(ou)h(expanz)-11
-b(\023)-38 b(\020)33 b(je)e Ff(V)2554 5662 y Fd(1)2594
-y Fh(,)g(p)s(o)g(adiabatic)m(k)m(\023)-46 b(e)32
-b(expanzi)h Ff(V)3713 5662 y Fd(2)3752 5647 y Fh(.)0
-y(T)-8 b(eplotu)44 b(plyn)m(u,)h(kter\023)-49 b(a)43
-b(b)m(y)h(m)m(\024)-46 b(ela)44 b(b)q(\023)-50 b(yt)44
-b(sho)s(dn\023)-49 b(a)43 b(s)h(teplotou)f(ok)m(ol)-11
-b(\023)-38 b(\020)44 b(b\023)-49 b(an)m(\024)j(e)43 b(rozum)-11
-b(\023)-38 b(\020me)45 b Ff(T)3345 5782 y Fd(1)3384 5767
-y Fh(.)e(Vnit)-5 b(\024)-43 b(rek)p Black Black eop end
+b(\023)-38 b(\020m)m(u)p Black Black eop end
 %%Page: 2 2
 TeXDict begin 2 1 bop 0 0 a
 SDict begin /product where{pop product(Distiller)search{pop pop pop version(.)search{exch pop exch pop(3011)eq{gsave newpath 0 0 moveto closepath clip/Courier findfont 10 scalefont setfont 72 72 moveto(.)show grestore}if}{pop}ifelse}{pop}ifelse}if end
 ,247 → 2066,342
 SDict begin H.R end
 -207 a 0 -207 a
 SDict begin [ /View [/XYZ H.V] /Dest (page.2) cvn H.B /DEST pdfmark end
--207 a Black Black 307 x Fh(b\023)-49
-b(an)m(\024)j(e)32 b(je)g(o)s(d)f(vn)m(\024)-46 b(ej)-5
-b(\024)-44 b(s)-11 b(\023)-38 b(\020ho)33 b(vzduc)m(h)m(u)h(o)s(dd)m
-(\024)-46 b(elen)32 b(mem)m(br\023)-49 b(ano)m(v)q(\023)f(ym)35
+-207 a Black Black 307 x Fh(barometric)m(k)m
+(\023)-46 b(em)m(u)40 b(tlaku)d Fg(b)h Fh(p)-5 b(\024)-43
+b(retlak)37 b Fg(h)p Fh(.)g(T)-8 b(en)38 b(o)s(de)m(\024)-46
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+(u)i(v)e(b\023)-49 b(ani)33 b(je)g(pak)1658 440 y Fg(p)1707
+y Fe(1)1774 440 y Fh(=)27 b Fg(b)c Fh(+)f Fg(h:)146
+y Fh(P)-5 b(\024)-43 b(r)-11 b(\023)-38 b(\020slu)-5
+b(\024)-44 b(sn)q(\023)-50 b(y)33 b(ob)5 b(jem)32 b(vzduc)m(h)m(u)i(p)
+-5 b(\024)-43 b(red)31 b(adiabatic)m(k)m(ou)h(expanz)-11
+b(\023)-38 b(\020)33 b(je)e Fg(V)2554 675 y Fe(1)2594
+y Fh(,)g(p)s(o)g(adiabatic)m(k)m(\023)-46 b(e)32
+b(expanzi)h Fg(V)3713 675 y Fe(2)3752 660 y Fh(.)0 781
+y(T)-8 b(eplotu)44 b(plyn)m(u,)h(kter\023)-49 b(a)43
+b(b)m(y)h(m)m(\024)-46 b(ela)44 b(b)q(\023)-50 b(yt)44
+b(sho)s(dn\023)-49 b(a)43 b(s)h(teplotou)f(ok)m(ol)-11
+b(\023)-38 b(\020)44 b(b\023)-49 b(an)m(\024)j(e)43 b(rozum)-11
+b(\023)-38 b(\020me)45 b Fg(T)3345 796 y Fe(1)3384 781
+y Fh(.)e(Vnit)-5 b(\024)-43 b(rek)0 901 y(b\023)-49 b(an)m(\024)j(e)32
+b(je)g(o)s(d)f(vn)m(\024)-46 b(ej)-5 b(\024)-44 b(s)-11
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 b(z\023)-49 b(av)m(\024)j(erem.)33 b(Otev)-5 b(\024)-43
 b(reme-li)32 b(jej)f(dostate)m(\024)-46 b(cn)m(\024)g(e)0
-y(ale)38 b(na)f(v)m(elmi)i(kr\023)-49 b(atk)m(ou)38
+y(ale)38 b(na)f(v)m(elmi)i(kr\023)-49 b(atk)m(ou)38
 b(dobu,)g(vyro)m(vna)5 b(j)-11 b(\023)-38 b(\020)40 b(se)e(tlaky)g
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 %%Trailer

 /dokumenty/PRA1/4-Poisson/poisson.tex
 ,15 → 17,20
 \end{abstract}
-\section{Úvod}
+\section{Pracovní úkoly}
 \begin{enumerate}
 \item Změřte kompresí plynu objem baňky systému s kmitajícím pístkem.
 \item Změřte Poissonovu konstantu metodou adiabatické expanze a současně metodou kmitajícího pístku.
 \item Oba výsledky porovnejte. Výsledek metody kmitajícího pístku považujte za tabulkovou hodnotu Poissonovy konstanty.
+\item Jednolitrovou láhev zvažte prázdnou.
+\item Jednolitrovou láhev zvažte plnou vody.
+\item Z obou výsledků určete objem lahve.
+\item Objem prázdné jednotlitrové lahve určete kompresí plynu.
+\item Stejným postupem změřte objem hadičky spojující byretu s měřeným prostorem. Tuto hodnotu odečtěte od výsledku podle bodu 7.
 \end{enumerate}
 \section{Úvod}
-\subsection{Modul pružnosti v tahu}
 Poissonova konstanta $\kappa $ je poměr měrného tepla $C_{P}$ při stálém tlaku ke měrnému teplu $C_{V}$ při stálém objemu
 \begin{displaymath} \kappa = \frac{C_P }{C_V }. \end{displaymath}
 ,7 → 70,12
 \begin{displaymath} \kappa=\frac{4mV}{T^2 pr^4} \end{displaymath}
 \section{Postup měření}
+\subsection{Měření dutých objemů}
+Dostali jsme za úkol změřit objem jisté zhruba jednolitrové lahve.  Lahev jsme proto připojili j plynové byretě a definovanou kompresí několika desítek $cm^3$ vzduchu jsme změřili její objem. Který i s přívodní hadičkou od byrety činil 1141,78 $cm^3$. K odečtení objemu hadičky byla využita stejná metoda s tím rozdílem, že jsme odpojili flašku a hadičku zašpuntovali.. Naměřili jsme tak objem hadičky 71,16 $cm^3$ po vzájemném odečtení těchto dvou objemů je výsledný objem lahve 1,07363 litru.
+Druhou metodou kterou jsme vyzkoušeli bylo zvážení prázdné lahve (0,56 kg) a po jejím naplnění vodou o téže teplotě (25 $^\circ C)$ její opětovné zvážení (1,58 kg) protože známe hustotu vody při této teplotě 995,72 $kg/m^3$. Můžeme spočítat objem lahve 1,02438 litru.
+\subsection{Měření Poissonovy konstanty plynu}
 Během měření Poissonovy konstanty Clement-Desormesovo metodou jsme se snažili o maximální zkrácení času otevření ventilu, po krátkém tréninku bylo jasné, že nemá smysl dobu otevření snižovat pod mez zhruba 70ms neboť se nestačí dostatečně vyrovnat tlak v aparatuře s atmosférickým tlakem.
 Uvedené výsledky jsou proto nad touto hranicí. Průměr z naměřených hodnot je $1,40 \pm 0,02$
 ,7 → 99,7
 V celém průběhu měření jsme paralelně měřili Poissonovu konstantu i pomocí kmitajícího pístu. A tabulka \ref{Kmit} udává naměřená i vypočtená data, jako objem baňky jsme zvolili asistentem doporučený objem $0,001067 m^3$ jelikož ho nebylo možné změřit žádným z v návodu \cite{objemy} popsaných postupů. Průměrnou změřenou hodnotou je $1,29 \pm 0,03 $. Ostatní konstanty potřebné pro výpočet jsou převzaté z návodu k úloze.
 \begin{table}[htbp]
-\caption{Pocty period pistu v petiminutovem mericim intervalu a vypoctena hodnota Poissovnovy konstanty}
+\caption{Pocty period pistu v pěti minutovém měřícím intervalu a vypočtená hodnota Poissovnovy konstanty}
 \begin{center}
 \begin{tabular}{|c|c|}
 \hline

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+end readonly def
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+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+dict begin
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+%!PS-AdobeFont-1.1: CMSY8 1.0
+%%CreationDate: 1991 Aug 15 07:22:10
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+dict begin
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+%%CreationDate: 1991 Aug 20 16:39:40
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+dict begin
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+%!PS-AdobeFont-1.1: CMSY10 1.0
+%%CreationDate: 1991 Aug 15 07:20:57
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+dict begin
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+%%BeginFont: CMMI8
+%!PS-AdobeFont-1.1: CMMI8 1.100
+%%CreationDate: 1996 Jul 23 07:53:54
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+dict begin
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+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMMI8) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.04 def
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+end readonly def
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+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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+dup 86 /V put
+dup 97 /a put
+dup 107 /k put
+dup 114 /r put
+dup 117 /u put
+dup 118 /v put
+readonly def
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+currentdict end
+currentfile eexec
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+%%BeginFont: CMMI12
+%!PS-AdobeFont-1.1: CMMI12 1.100
+%%CreationDate: 1996 Jul 27 08:57:55
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+dict begin
+/FontInfo 7 dict dup begin
+/version (1.100) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMMI12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle -14.04 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMMI12 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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+readonly def
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+currentdict end
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+cleartomark
+%%EndFont
+%%BeginFont: CMR12
+%!PS-AdobeFont-1.1: CMR12 1.0
+%%CreationDate: 1991 Aug 20 16:38:05
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+dict begin
+/FontInfo 7 dict dup begin
+/version (1.0) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMR12) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMR12 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
+/Encoding 256 array
+1 255 {1 index exch /.notdef put} for
+dup 1 /Delta put
+dup 12 /fi put
+dup 16 /dotlessi put
+dup 19 /acute put
+dup 20 /caron put
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+dup 117 /u put
+dup 118 /v put
+dup 119 /w put
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+readonly def
+/FontBBox{-34 -251 988 750}readonly def
+currentdict end
+currentfile eexec
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+%%EndFont
+%%BeginFont: CMR10
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+%%CreationDate: 1992 Feb 19 19:54:52
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+dict begin
+/FontInfo 7 dict dup begin
+/version (1.00B) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
+/FullName (CMR10) readonly def
+/FamilyName (Computer Modern) readonly def
+/Weight (Medium) readonly def
+/ItalicAngle 0 def
+/isFixedPitch false def
+end readonly def
+/FontName /CMR10 def
+/PaintType 0 def
+/FontType 1 def
+/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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+dup 19 /acute put
+dup 20 /caron put
+dup 39 /quoteright put
+dup 45 /hyphen put
+dup 46 /period put
+dup 90 /Z put
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+readonly def
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+currentdict end
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+%%CreationDate: 1992 Feb 19 19:54:06
+% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
+dict begin
+/FontInfo 7 dict dup begin
+/version (1.00B) readonly def
+/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
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+/Weight (Bold) readonly def
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+/isFixedPitch false def
+end readonly def
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+dup 114 /r put
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+readonly def
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+SDict begin H.S end
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+SDict begin H.S end
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+SDict begin H.S end
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+SDict begin H.S end
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+SDict begin H.S end
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+SDict begin H.S end
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+SDict begin 14.5 H.A end
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+TeXDict begin 2 1 bop 0 0 a
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 /dokumenty/PRA1/5-Teplomer/teplomer.tex
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+\documentclass[12pt,a4paper,oneside]{article}
+\usepackage[colorlinks=true]{hyperref}
+\usepackage[utf8]{inputenc}
+\usepackage[czech]{babel}
+\usepackage{graphicx}
+\textwidth 16cm \textheight 24.6cm
+\topmargin -1.3cm
+\oddsidemargin 0cm
+\pagestyle{empty}
+\begin{document}
+\title{Kalibrace rtuťového teploměru plynovým teploměrem}
+\author{Jakub Kákona, kaklik@mlab.cz}
+\date{30.11.2009}
+\maketitle
+\thispagestyle{empty}
+\begin{abstract}
+Zkalibrovali jsme rtuťový teploměr pomocí plynového teploměru. Získané hodnoty jsme zároveň použili k určení součinitele rozpínavosti vzduchu.
+\end{abstract}
+\section{Pracovní úkoly}
+\begin{enumerate}
+\item Ocejchujte rtuťový teploměr pomocí plynového teploměru a nakreslete příslušný graf.
+\item Vypočítejte součinitele rozpínavosti plynů $\gamma $ a proveďte kontrolu pomocí teploty absolutní nuly.
+\item  Určete tepelnou kapacitu kalorimetru (Dewarovy nádoby), který použijete při určování měrného skupenského tepla varu vody. Sestrojte z naměřených hodnot graf závislosti teploty lázně na čase. Posuďte, zda tento postup je pro daný kalorimetr nutný.
+\item  Určete měrné skupenské teplo varu vody s ohledem na množství předčasně zkondenzované páry $m_{v}$.
+\end{enumerate}
+\section{Úvod}
+Teplota varu vody je dána výrazem
+\begin{equation}
+ t_{varu} = 100,000 + 0,03687 (b - 760) - 0,000 022 (b - 760)^{2} [ ^\circ C, Torr].
+\end{equation}
+Následně pak dokážeme určit i teplotu na plynovém teploměru.
+\begin{equation}
+ t = t_{varu}\frac{\Delta h}{\Delta h_{varu}}.
+\end{equation}
+Hodnoty můžeme také využít k dopočítání rozpínavosti vzduchu
+\begin{equation}
+ \gamma = \frac{1}{p}\left( \frac{\partial }{\partial T} \right)_{V} \simeq \frac{\Delta p}{p} \frac{1}{\Delta T}.
+\end{equation} což můžeme přepsat na
+\begin{equation} \gamma = \frac{\Delta h}{b\cdot t}, \label{egamma}\end{equation}
+kde b je atmosfericky tlak v Torrech.
+Při měření skupenského tepla varu vody využijeme kalorimetrickou rovnici.
+\begin{equation}
+ (m-m_{v})l_{v}+mc(t_{varu} -t)+(m_kc+\kappa)(t_{0}-t)=0,
+\end{equation} kde $c$ je měrná tepelná kapacita vody. Měrné skupenské teplo varu pak vyjádříme jako
+\begin{equation}
+ l_{v}=\frac{(m_{k}+\kappa)(t-t_{0})-mc(t_{varu}-t) }{m-m_{v}}. \label{elv}
+\end{equation}
+Chybí nám ale tepelná kapacita kalorimetru, kterou musíme změřit. K tomu nám pomůže jiná kalorimetrická rovnice
+\begin{equation}
+ (m_{1}c+\kappa)(t_{1}-t)+m_{2}c(t_{2}-t)=0,
+\end{equation} ze které vyjádříme kapacitu kalorimetru.
+\begin{equation}
+ \kappa = \frac{m_{2}c(t-t_{2})}{(t_{1}-t)}-m_{1}c. \label{ekappa}
+\end{equation}
+\section{Postup měření}
+\subsection{Kalibrace rtuťového teploměru plynovým teploměrem}
+Nejdříve jsme měřící bańku plynového teploměru ochladili při atmosférickém tlaku uvnitř, po vyrovnání teplot jsme uzavřeli ventil spojující vnitřní objem teploměru s vnější atmosférou a začali postupně zvyšovat teplotu lázně zhruba po 10 $^\circ C$. Vždy při odečítání hodnot ale bylo nutné udržovat konstantní objem plynu v teploměru což bylo zařízeno udržováním hladiny rtuti v otevřeném manometru na špičce skleněného hrotu.
+Během měření byl atmosférický tlak $b = (743,6 \pm 0,1) Torr$ . Naměřenou závislost jsme vynesli do grafu \ref{korekce}. A tím zjistili směrnici přímky $a = (2,5 \pm 0,05) m/^\circ C$ a spočítali tak i rozpínavost vzduchu $a = (3,48 \pm 0,07)10^{-3} /K$.
+\begin{table}[htbp]
+\begin{center}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline
+$h_l [mm]$ & $t_s [^\circ C]$ & $\Delta h [mm]$ & $t_m [^\circ C]$ & $\Delta t [^\circ C]$ & $\delta_t [\%]$ \\ \hline
+& 0,0 & 0 & 0,0 & 0 & 0 \\ \hline
+& 11,2 & 29 & 12,1 & -0,86 & 7,13 \\ \hline
+& 24,2 & 64 & 26,6 & -2,41 & 9,07 \\ \hline
+& 30,1 & 80 & 33,3 & -3,17 & 9,52 \\ \hline
+& 43,2 & 119 & 49,5 & -6,29 & 12,7 \\ \hline
+& 62,2 & 165 & 68,6 & -6,42 & 9,35 \\ \hline
+& 72,0 & 191 & 79,4 & -7,43 & 9,35 \\ \hline
+& 87,2 & 204 & 84,8 & 2,37 & 2,79 \\ \hline
+& 99,39 & 239 & 99,39 & 0 & 0 \\ \hline
+\end{tabular}
+\end{center}
+\caption{Kalibrace rtutového teploměru plynovým teploměrem}
+\label{kalibrace}
+\end{table}
+\begin{figure}
+\begin{center}
+\includegraphics [width=150mm] {teplomer_char.pdf}
+\end{center}
+\caption{Hodnoty naměřené na plynovém a rtuťovém teploměru}
+\label{korekce}
+\end{figure}
+\subsection{Měření měrného skupenského tepla varu vody}\
+K tomuto měření bylo třeba nejdříve změřit tepelnou kapacitu kalorimetru, použili jsme v návodu doporučenou metodu a kapacita nám vyšla $\kappa = (90 \pm 7) J/kg K$.  S touto znalostí, jsme pak již nechali ohřívat vodní náplň v kalorimetru párou probublávající z kotlíku s vroucí vodou. Po změření rozdílu teplot a zvážení zkondenzované vody jsme pak mohli určit měrné skupenské teplo varu vodu jako $l_v = (2,6 \pm 0,3) MJ/kg$.
+\section{Diskuse}
+V návodu k úloze \cite{var_vody} je doporučen postup měření tepelné kapacity kalorimetru využívající časovou závislost vývoje teploty. Vzhledem k našim podmínkám je ale tento postup zbytečně přesný (Máme dobře izolovaný kalorimetr).
+\section{Závěr}
+Součinitel rozpínavosti plynů jsme určili s relativní chybou 4,9 \% vzhledem k tabulkové hodnotě. A měrné skupenské teplo varu vody jsme proti tabulkové hodnotě $l_v = 2,257 MJ/kg$ určili s chybou 15\%.
+\begin{thebibliography}{99}
+\bibitem{var_vody}{Zadání úlohy 5 - Měření měrného skupenského tepla varu vody}. \href{http://praktika.fjfi.cvut.cz/SkupTepVaru/}{http://praktika.fjfi.cvut.cz/SkupTepVaru/}
+\end{thebibliography}
+\end{document}

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