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%