PHYSICAL CHEMISTRY IN BRIEF

CHAP. 4: APPLICATION OF THERMODYNAMICS [CONTENTS] 120

AHeat pumpis a device consisting of a cooling engine and a warmer reservoir of tem-
peratureT 2. The surroundings represent the cooler reservoir of temperatureT 1. A heat pump
serves for the heating of a room using heat absorbed from, e.g. a cooler stream. Both in the case
of a refrigerator and in the case of a heat pump, work is consumed on heat transfer from the
cooler to the warmer place. The difference between the two devices rests only in the purpose
to which they serve.

Example

Let us imagine a cottage whose temperature inside isT 2 = 290 K, and a nearby stream of

temperatureT 1 = 277 K. The cottage is not adiabatically insulated from its surroundings, and

consequently the heatQhas to be supplied per a time unit in order to maintain constant tem-

perature in the rooms. Prove that it is cheaper to heat the cottage using a heat pump than using

an electric storage heater.

Proof

When using a heat pump, the heatQsupplied to the cottage equals the sum of workW and

heatQ 1 supplied to the pump,Q=W +Q 1. From this and from (4.32) and (4.33) it follows

that

W=Q

T 2 −T 1

T 2

=

Q

22. 3

When a heat pump is used, the electric energy needed for heating equalsW. In the case of

an electric storage heater converting electric energy into heat, it equalsQ. In terms of electric

energy consumption, a heat pump comes 22.3×cheaper under the given conditions.

4.3.3 Heat engine with steady flow of substance

A heat engine with a steady flow of substance is a device that exchanges shaft workWshwith
its surroundings at the cost of the energy of the working medium flow.
From the energy balance applied to a steady state (while neglecting the potential and kinetic
energy of the current) we have

U 1 +p 1 V 1 +Wsh+Q=U 2 +p 2 V 2. (4.34)