A carnot engine takes in 3000 kcal 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:

Carnot Engine

A Carnot engine is an idealized thermodynamic engine that operates on the Carnot cycle. It is the most efficient possible engine, as it works on reversible processes.

The efficiency of a Carnot engine depends on the temperatures of the heat source and the heat sink.

EXPLANATION:

Given:

Heat absorbed from the reservoir (Q_H) = 3000 kcal

Temperature of the heat source (T_H) = 627°C = 900 K

Temperature of the heat sink (T_C) = 27°C = 300 K

The efficiency of a Carnot engine is given by:

η = 1 - (T_C/T_H)

Substitute the values to find the efficiency:

η = 1 - (300/900)

η = 1 - 1/3

η = 2/3

Work done by the engine (W) is given by:

W = η × Q_H

Q_H in joules = 3000 kcal × 4184 J/kcal = 12552 × 10³ J

W = (2/3) × 12552 × 10³ J

W = 8370.66 × 10³ J ≈ 8.4 × 10⁶ J

Therefore, the correct answer is option 2: 8.4 × 10⁶ J.