Question

A monoatomic gas is used in a Carnot engine as the working substance, If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 8V₁ the efficiency of the engine is .. 

(A) 60% 

(B) 50% 

(C) 75% 

(D) 25%

Answer 1

Correct option: (C) 75%

Explanation:

Efficiency of cannot engine = η = 1 – (T₂ / T₁)…….(1)

Given is adiabatic process hence (T₁ / T₂) = (V₂ / V₁)^(γ–1)……….(2)

For mono atomic gas, γ = (5/3)

Hence from (2),       (T₁ / T₂) = (V₂ / V₁)^[(5/3)–1] 

Given V₁ = V

V₂ = 8V

Hence (T₁ / T₂) = (8V / V)^2/3 

(T₁ / T₂) = 2^[3×(2/3)] 

(T₁ / T₂) = 4

From (1) η = 1 – (T₂ / T₁) = [1 – (1/4)] = 3/4

% efficiency = % η = (3/4) × 100 = 75%