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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 82.82J
As the process is done suddenly,

It is adiabatic process,(γ=1.5)

TVγ1=constant

T1=300K,
By the above relationship, T2=3002K

And as P1=100kPa

n=PVRT=100×103Pa×103m3300R

W=ΔU=nRΔTγ1=13R×R×300(21)0.5

W=200(21)=82.82 J

Option A is the correct answer.

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