Question

A monoatomic gas ( = 5/3) at pressure p is suddenly compressed to its volume adiabotically. What is pressure of the compressed gas .

Answer 1

A monoatomic gas for it γ = (5 / 3) is suddenly Compressed

to (1 / 8) of its original volume adiabatically then the final

Pressure of gas is ............. times its initial Pressure.

(A) 8 (B) 32 (C) (24 / 5) (D) (40 / 3)

Solution: Answer: (B) 32

under adiabatic condition

PVγ = constant

∴ (P1 / P2) = (V2 / V1)γ

given = V2 = (V1 / 8) γ = (5/3)

∴ (P1 / P2) = [(V1 × 1) / (8 × V1)]5/3

(P1 / P2) = (1/8)5/3 = [1 / (2){3×(5/3)}] = (1/25)

∴ P2 = 32 P1­

i.e. final pressure is 32 times of initial pressure.