Thermodynamics Question 48
Question: A gas for which $ \gamma =1.5 $ is suddenly compressed to$ \frac{1}{4} $ th of the initial volume. Then the ratio of the final to the initial pressure is
[EAMCET 2001]
Options:
A) Lesss than P
B) More than P
C) P
D) Either (a) or (c)
Show Answer
Answer:
Correct Answer: B
Solution:
$ P{{V}^{\gamma }}= $ constant
Therefore $ \frac{P _{2}}{P _{1}}={{( \frac{V _{1}}{V _{2}} )}^{\gamma }}={{( \frac{V _{1}}{V _{1}/4} )}^{\gamma }}={{4}^{\gamma }} $
Therefore $ P _{2}={{4}^{\gamma }}P $
As g is always greater than one so $ {{4}^{\gamma }}>4 $
Therefore $ P _{2}>4P $
