PHYSICAL CHEMISTRY IN BRIEF

CHAP. 4: APPLICATION OF THERMODYNAMICS [CONTENTS] 115

4.3 Heat engines.

Aheat engineis a device that cyclically converts heat into work. According to the Second
Law of thermodynamics, this conversion cannot be complete [see3.1.3]. In the strict sense
of the word, a heat engine means a device that cyclically receives heatQ 2 (Q 2 >0) from the
warmer reservoir of temperatureT 2. It converts part of it into workWdone=−W, which it
supplies to the surroundings. At the same time it supplies heatQsupplied=−Q 1 (Q 1 <0) to the
cooler reservoir of temperatureT 1 , and returns to the initial state. During this cyclic process,
the change of internal energy is zero, and consequently we have

Q 1 +W+Q 2 = 0.

Example

A heat engine received 600 J of heat from the warmer reservoir, supplied 500 J of heat to the

cooler reservoir, and returned to the initial state. Ascertain the work performed by the engine.

Solution

It follows from the specification thatQ 1 = 600 J,Q 2 =−500 J,Q=Q 1 +Q 2 = 100 J. Since

the system returned to its original state,∆U = 0. From equation (4.13) we thus have

W=−Q=− 100 J.

The workperformed by the engineisWdone=−W=−(− 100 J) = +100J.

4.3.1 The Carnot heat engine

Let the temperature of the warmer reservoir beT 2 and that of the cooler reservoir beT 1. One
cycle is comprised of four partial reversible processes:

(a) isothermal expansion at temperatureT 2

(b)adiabatic expansion from temperatureT 2 to temperatureT 1

(c) isothermal compression at temperatureT 1

(d)adiabatic compression from temperatureT 1 to the initial point.