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Question

# 1 litre of an ideal gas (γ=1.5) at 300 K is suddenly compressed to half its original volume.If the original pressure is 100 kPa, find the work done by the gas in the process.Take: √2=1.41

A
82.82J
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B
92.47J
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C
72.47J
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D
42.47J
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Solution

## The correct option is B −82.82JAs the process is done suddenly,It is adiabatic process,(γ=1.5)TVγ−1=constantT1=300K, By the above relationship, T2=300√2KAnd as P1=100kPan=PVRT=100×103Pa×10−3m3300RW=−ΔU=−nRΔTγ−1=13R×R×300(√2−1)0.5W=−200(√2−1)=−82.82 JOption A is the correct answer.

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