110 Problems d Sdutioru on Thermcdynamice d Statistical Mechanica
With TI = 300 K, Tz = 273 K, we find
= 1.3 x lo3.
1112
Compute the theoretical minimum amount of mechanical work needed
to freeze 1 kilogram of water, if the water and surroundings are initially at
a tempera.ture To = 25°C. The surroundings comprise the only large heat
reservoir available.
(Lice = 80 cal/g, C, =^1 cal/g. O C).
(UC, Berkeley)
Solution:
The minimum work can be divided into two parts W1 and Wz: W1 is
used to lower the water temperature from 25OC to O"C, and W2 to transform
water to ice. We findW1 = - (To - T)MC,dT/T
ITo
= MCpTo ln(To/Tr) - MC,(To - Z)
= 1.1 x lo3 cal ,
W2 = (TO - Tf)LM/Tf = 7.3 x lo3 cal ,
W = W1 + W2 = 8.4 x lo4 cal = 3.5 x lo4 J.111s
An ideal Carnot refrigerator (heat pump) freezes ice cubes at the rate
of 5 g/s starting with water at the freezing point. Energy is given off to
the room at 3OoC. If the fusion energy of ice is 320 joules/gram,
(a) At what rate is energy expelled to the room?
(b) At what rate in kilowatts must electrical energy be supplied?
(c) What is the coefficient of performance of this heat pump?
( wzs co nsin)