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Question

An ideal monatomic gas at 300 K expands adiabatically to 8 times its volume. What is the final temperature?

A
75 K
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B
300 K
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C
560 K
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D
340 K
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Solution

The correct option is A 75 K
Given,
Gas is ideal and monoatomic, so γ=53
Gas is undergoing adiabatic expansion, so the equation of state of the gas in terms of T and V is given by
T Vγ1=k
From this, we can write that
TiVγ1i=TfVγ1f
or Tf=Ti(ViVf)γ1
From the data given in the question,
Tf=300×(Vi8Vi)531=3004=75 K
Hence, option (a) is the correct answer.

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