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

Concept:

The efficiency of a Carnot engine is determined by the temperatures of the hot and cold reservoirs.

1. Efficiency (η) = 1 - (T_cold / T_hot)

2. Work done (W) = Q_in × η

Calculation:

Given:

Q_in = 3 × 10⁶ cal

T_hot = 627ºC = 627 + 273 = 900 K

T_cold = 27ºC = 27 + 273 = 300 K

⇒ Efficiency (η) = 1 - (T_cold / T_hot)

⇒ η = 1 - (300 / 900)

⇒ η = 1 - (1 / 3)

⇒ η = 2 / 3

1 cal = 4.2 J

⇒ Q_in = 3 × 10⁶ cal × 4.2 J/cal

⇒ Q_in = 12.6 × 10⁶ J

⇒ Work done (W) = Q_in × η

⇒ W = 12.6 × 10⁶ J × 2 / 3

⇒ W = 8.4 × 10⁶ J

∴ The work done by the engine is 8.4 × 10⁶ J.