Thermodynamics and Chemistry

CHAPTER 5 THERMODYNAMIC POTENTIALS

PROBLEMS 148

liquid

gas

Figure 5.2

pressure equal to the vapor pressure of the liquid,2:50 105 Pa, and some of the liquid vapor-

izes. Assume that the process is adiabatic and thatTandpremain uniform and constant. The

final state is described by

V 2 D0:2400m^3 T 2 D300:0K p 2 D2:50 105 Pa

(a)Calculateq,w,ÅU, andÅH.

(b)Is the process reversible? Explain.

(c)Devise a reversible process that accomplishes the same change of state, and use it to

calculateÅS.

(d)Compareqfor the reversible process withÅH. Does your result agree with Eq.5.3.8?

Table 5.1 Surface tension

of water at 1 bara

t=C 

=10^6 J cm^2

15 7:350

20 7:275

25 7:199

30 7:120

35 7:041

aRef. [ 163 ].

5.6 Use the data in Table5.1to evaluate.@S=@As/T;pat 25 C, which is the rate at which the

entropy changes with the area of the air–water interface at this temperature.

5.7 When an ordinary rubber band is hung from a clamp and stretched with constant downward

forceFby a weight attached to the bottom end, gentle heating is observed to cause the rubber

band to contract in length. To keep the lengthlof the rubber band constant during heating,

Fmust be increased. The stretching work is given by∂w^0 DFdl. From this information,

find the sign of the partial derivative.@T=@l/S;p; then predict whether stretching of the rubber

band will cause a heating or a cooling effect.

(Hint: make a Legendre transform ofUwhose total differential has the independent variables

needed for the partial derivative, and write a reciprocity relation.)

You can check your prediction experimentally by touching a rubber band to the side of your

face before and after you rapidly stretch it.