Thermodynamics Question 263
Question: One mole of an ideal gas at an initial temperature of T K does 6R joules of word adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, the final temperature of gas will be
Options:
A) $ (T-4)K $
B) $ (T+2.4)K $
C) $ (T-2.4)K $
D) $ (T+4)K $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ T _{1}=T,W=6R\text{ joules},\gamma =\frac{5}{3} $
$ W=\frac{P _{1}V _{1}-P _{2}V _{2}}{\gamma -1}=\frac{nRT _{1}-nRT _{2}}{\gamma -1} $
$ =\frac{nR( T _{1}-T _{2} )}{\gamma -1} $
$ n=1,T _{1}=T\Rightarrow \frac{R( T-T _{2} )}{5/3-1}=6R $
$ \Rightarrow T _{2}=( T-4 )K $
