Question

A Carnot engine takes 3 × 10⁶ cal of heat from a reservoir at 627° C, and gives to a sink at 27° C. The work done by the engine is 

(A) 4.2 × 10⁶J 

(B) 16.8 × 10⁶J 

(C) 8.4 × 10⁶J 

(D) Zero

Answer 1

Correct option: (C) 8.4 × 10⁶J

Explanation:

Given:  Q = 3 × 10⁶ cal = 3 × 4.2 × 10⁶ J…….as 1 cal = 4.2 J

T₁ = 627 °C = 627 + 273 = 900K

T₂ = 27 °C = 27 + 273 = 300K

As η = [1 – (T₂ / T₁)]

η = [1 – (300 / 900)] = (2/3)

As  work done = W = η ∙ Q

∴  W = (2/3) × (3 × 10⁶) × 4.2

W = 8.4 × 10⁶ J