Problems and Solutions on Thermodynamics and Statistical Mechanics

Thermodyzamics 35

The energy it gives to the source of lower temperature is Qgi = c,(Tc - Td).
Thus

From the equation of state pV = nRT and the adibatic equations

P2Vd' = PlVJ , p2v: = p1v; ,

we have

(b) From the state equation, we know Tb > T,,Tc > Td; from the
adiabatic equation, we know Tb > Tc, T, > Td; thus

1039

A building at absolute temperature T is heated by means of a heat

pump which uses a river at absolute temperature To as a source of heat.

The heat pump has an ideal performance and consumes power W. The

building loses heat at a rate cr(T - To), where Q is a constant.

(a) Show that the equilibrium temperature T, of the building is given

by

Te=To+w 2a [1+ (1+9)']

(b) Suppose that the heat pump is replaced by a simple heater which

also consumes a constant power W and which converts this into heat with

100% efficiency. Show explicitly why this is less desirable than a heat pump.

(Columbia)