Thermodynamics Question 5
Question: A monoatomic gas $ (\gamma =5/3) $ is suddenly compressed to $ \frac{1}{8} $ of its original volume adiabatically, then the pressure of the gas will change to
[CPMT 1976, 83; MP PMT 1994; DPMT 1996; Roorkee 2000; KCET 2000; Pb. PMT 1999, 2001]
Options:
A) 4 atmosphere
B) $ \frac{3}{2} $ atmosphere
C) 8 atmosphere
D) $ \frac{1}{4} $ atmosphere
Show Answer
Answer:
Correct Answer: C
Solution:
$ 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 $ .
