Problems and Solutions on Thermodynamics and Statistical Mechanics

66 Problem d Solution, on Thermodynamics d Statistical Mechanica

• W,,, corresponds to Tfn,in, i.e., the reversible heat engine has the maxi-
  mum delivered work

1070
One kilogram of water is heated by an electrical resistor from 20°C to
99°C at constant (atmospheric) pressure. Estimate:
(a) The change in internal energy of the water.
(b) The entropy change of the water.
(c) The factor by which the number of accessible quantum states of

(d) The maximum mechanical work achievable by using this water as

(UC, Berkely)

the water is increased.

heat reservoir to run an engine whose heat sink is at 20°C.

Solution:

(a) The change in internal energy of the water is

AU = McAT = 1000 x 1 x 79 = 7.9 x lo4 cal.

(b) The change in entropy is

AS = s -dT Mc = Mc In - T2 = 239 cal/K,

T Tl

(c) Rom Boltzmann’s relation S = Iclnr2, we get

nl

• n2 = exp (y) = exp(7 x 1025).

(d) The maximum mechanical work available is

= 9 x lo3 cal.