Thermodynamics Question 40
Question: If $ \gamma =2.5 $ and volume is equal to $ \frac{1}{8} $ times to the initial volume then pressure P’ is equal to (Initial pressure = P)
[RPET 2003]
Options:
A) $ {{27.5}^{o}}C $
B) $ 75^{o}K $
C) $ 150K $
D) $ 150^{o}C $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{T _{2}}{T _{1}}={{( \frac{P _{2}}{P _{1}} )}^{\frac{\gamma -1}{\gamma }}} $
$ \Rightarrow \frac{T _{2}}{T _{1}}={{( \frac{1}{8} )}^{\frac{1.5-1}{1.5}}}={{( \frac{1}{8} )}^{\frac{1}{3}}}=\frac{1}{2} $
$ \Rightarrow T _{2}=\frac{T _{1}}{2}=\frac{300}{2}=150K $ .
