Thermodynamics Question 4

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

[BHU 1995]

Options:

A) $ 300{{(4)}^{1.4/0.4}} $

B) $ 300{{( \frac{1}{4} )}^{-0.4/1.4}} $

C) $ 300{{(2)}^{-0.4/1.4}} $

D) $ 300{{(4)}^{-0.4/1.4}} $

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Answer:

Correct Answer: D

Solution:

For adiabatic process $ \frac{{{T}^{\gamma }}}{{{P}^{\gamma -1}}}= $ constant

Therefore $ \frac{T _{2}}{T _{1}}={{( \frac{P _{1}}{P _{2}} )}^{\frac{1-\gamma }{\gamma }}} $

Therefore $ \frac{T _{2}}{300}={{( \frac{4}{1} )}^{\frac{(1-1.4)}{1.4}}} $

Therefore $ T _{2}=300{{(4)}^{-\frac{0.4}{1.4}}} $



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