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)

Answer 1

From the equation for the adiabatic process,

PV^γ = constant

Using differentiation, we get

Pγ V^{γ − 1} dV + dP.V^γ = 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%