Kinetic Theory Of Gases Question 167
Question: A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats $ \gamma $ . It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by
Options:
A) $ \frac{(\gamma -1)}{2(\gamma +1)R}Mv^{2}K $
B) $ \frac{(\gamma -1)}{2\gamma }Mv^{2}K $
C) $ \frac{\gamma Mv^{2}}{2R}K $
D) $ \frac{(\gamma -1)}{2R}Mv^{2}K $
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Answer:
Correct Answer: D
Solution:
[d] $ \frac{1}{2},Mv^{2}=1\cdot C _{V}\Delta T $
$ \Rightarrow $ $ \frac{1}{2}Mv^{2}=\frac{R}{\gamma -1}.\Delta T $
$ \Rightarrow $ $ \Delta T=\frac{Mv^{2}(\gamma -1)}{2R}=\frac{(\gamma -1)Mv^{2}}{2R} $
BETA
