Thermodynamics Question 359
Question: A gas at NTP is suddenly compressed to one-fourth of its original volume. If $ \gamma $ is supposed to be $ \frac{3}{2} $ , then the final pressure is
Options:
A) 4 atmosphere
B) $ \frac{3}{2} $ atmosphere
C) 8 atmosphere
D) $ \frac{1}{4} $ atmosphere
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ P{{V}^{\gamma }}=\text{constant}\Rightarrow \frac{P _{2}}{P _{1}}={{( \frac{V _{1}}{V _{2}} )}^{\gamma }} $
$ \Rightarrow \frac{P _{2}}{1}={{( \frac{V _{1}}{V _{1}/4} )}^{3/2}}=8 $
Therefore $ P _{2}=8\ atm $ .
