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Question

A sample of gas (γ=1.5) is taken through an adiabatic process in which the volume is compressed from 2000 cm3 to 500 cm3. If the initial pressure is 120 kPa, then:


A
The final pressure at point 2 is 960 kPa.
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B
Heat transferred, ΔQ12=0.
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C
Work done on the gas is 480 J.
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D
The final pressure at point 2 is 480 kPa.
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Solution

The correct option is C Work done on the gas is 480 J.
For an adiabatic process,
P1Vγ1 = P2Vγ2
[P=Pressure and V=Volume]
P2=P1(V1V2)γ=120×(2000500)1.5=960 kPa

Work done in adiabatic process is
W=P1V1P2V2γ1=(120×103)(2000×106)(960×103)(500×106)1.51=480 J

So, work done on the gas is 480 J
Also, heat transferred in adiabatic process is always zero.
Hence, options (a), (b), (c) are correct.

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