An ideal diatomic gas under goes a process in which it internal energy changes with volume as given U - CV 2-5 where c is constant- Find the ratio of molar heat capacity of the process to universal gas constant R-

For a process PV^x =constant, we have the specific Heat as C=R/r 1+R/1 x We have U=CV^2/5⋯(1) But u=nC_vT=nC_v [ PV/nR ]=R PV (k = constant) RPV = CV^2/5 Or PV^ ...

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Standard XII

Physics

Specific Heat Capacity

An ideal diat...

Question

An ideal diatomic gas under goes a process in which it internal energy changes with volume as given $U = c V^{\frac{2}{5}}$ where c is constant. Find the ratio of molar heat capacity of the process to universal gas constant R.___

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Solution

For a process $P V^{x}$ =constant, we have the specific
$H e a t a s C = \frac{R}{r - 1} + \frac{R}{1 - x}$
$W e h a v e U = C V^{\frac{2}{5}} \dots (1)$
$B u t u = n C_{v} T = n C_{v} [\frac{P V}{n R}] = R P V (k = c o n s t a n t)$
$R P V = C V^{\frac{2}{5}}$
$O r P V^{\frac{3}{5}} = R^{1}$
$T h u s C = \frac{R}{\frac{7}{5} - 1} + \frac{R}{1 - \frac{3}{5}} = \frac{5 R}{2} + \frac{5 R}{2} = 5 R \Rightarrow \frac{C}{R} = 5$

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An ideal diatomic gas under goes a process in which it internal energy changes with volume as given U=cV25 where c is constant. Find the ratio of molar heat capacity of the process to universal gas constant R.___

For a process PVx =constant, we have the specific Heat as C=Rr−1+R1−x We have U=CV25⋯(1) But u=nCvT=nCv[PVnR]=R PV (k=constant) RPV=CV25 Or PV35=R1 Thus C=R75−1+R1−35=5R2+5R2=5R⇒CR=5

An ideal diatomic gas under goes a process in which it internal energy changes with volume as given $U = c V^{\frac{2}{5}}$ where c is constant. Find the ratio of molar heat capacity of the process to universal gas constant R.___