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Question
In an adiabatic expansion of the air, the volume is increased by 4%, what is the percentage change in pressure? (For air γ = 1.4)
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Solution
From the equation for the adiabatic process,
PVγ = constant
Using differentiation, we get
Pγ Vγ − 1 dV + dP.Vγ = 0
`"dP"/"P" = -γ "dV"/"V"`
Volume 'V' is increased by 4% and γ = 1.4
`"dP"/"P" xx 100 = -γ ("dV"/"V" xx 100)`
= − 1.4 × 4
= − 5.6
Pressure is decreased by 5.6%
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