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Question

In an adiabatic process, pressure is increased by 23%. If CPCV=32, then the volume decreases by about

A
49%
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B
23%
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C
4%
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D
94%
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Solution

The correct option is A 49%
For an adiabatic process, PVγ=K
Here, γ=CPCV=32 and K=constant
PV3/2=K
Taking log both sides,
logP+32logV=logK
On differentiating both sides using chain rule,
1P×dP+321V×dV=0
For finite differences in values of P and V, we can write above equation as,
ΔPP+32ΔVV=0
ΔVV=23ΔPP
ΔVV×100=(23)(ΔPP×100)
ΔVV×100=23×23=49%
Volume decreases by about 49%

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