Thermodynamics Question 249
Question: What will be the final pressure if an ideal gas in a cylinder is compressed adiabatically to $ \frac{1}{3}rd $ of its volume?
Options:
A) Final pressure will be three times less than initial pressure.
B) Final pressure will be three times more than initial pressure.
C) Change in pressure will be more than three times the initial pressure.
D) Change in pressure will be less than three times the initial pressure.
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Answer:
Correct Answer: C
Solution:
[c] $ P _{1}V _{1}^{\gamma }=P _{2}V _{2}^{\gamma } $ (Adiabatic change) $ P _{2}=P _{1}{{( \frac{V _{1}}{V _{2}} )}^{\gamma }}=P _{1}{{( \frac{V _{1}}{V _{1}/3} )}^{\gamma }}=P _{2}{{( 3 )}^{\gamma }} $
