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=P1V1−P2V2γ−1=(120×103)(2000×10−6)−(960×103)(500×10−6)1.5−1=−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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