Physical Chemistry Third Edition

3.3 The Calculation of Entropy Changes 129

Massive

object at

temperature

T 1

Massive

object at

temperature

T 2

Thin

connecting

bar

Adiabatic

insulation

(b)

(a)

X

T

T 2

T 1

Figure 3.9 An Example Irreversible Process.(a) The system. (b) The temperature dis-

tribution in the system.

The state of the system does not change during the process. The entropy change of the

universe is

∆Suniv∆Ssurr

The time rate of change of the entropy of the universe is called theentropy produc-

tion.Think of it as the rate at which new entropy is being generated. For our steady-state

process, the entropy production is

dSuniv

dt



(

dq

dt

)(

1

T 1

−

1

T 2

)



(

dq

dt

)(

∆T

T 1 T 2

)

(3.3-12)

wheredq/dtis the rate at which heat is transferred and where∆TT 2 −T 1. The

entropy production is the product of two factors. The first factor,dq/dt, represents the

rate of the process, and the second factor,∆T/(T 1 T 2 ), represents the driving force of

the process.

Exercise 3.12

For the system of Figure 3.9, calculate the rate of entropy production if the first object is at 325 K

and the second object is at 375 K, and if 200.0 J of heat flows in 30.0 s.