Question

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)

Answer 1

Correct option: (B) 32

Explanation:

Under adiabatic condition

PV^γ = 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.