As a second example, we consider the production of heat in a body by friction,
generated by a work input, −W. The body is again kept under isobaric condition. This
frictional irreversible process also results in an increase of entropy: Input to the body is
in the form of workflow and the part of the body that is affected by frictional entropy
production transformation of work into heat will experience increase in temperature
ÀW ¼ U B À U A ¼
Z B
A
@U
@T
p
dT
It will be shown in Chap. 9 that the following property relation applies:
@U
@T
p
¼ C p À pVb % C p ;
where the approximation applies for the body of substance with a negligible thermal
expansion coefficient b. The final temperature is then
T B ¼ T A þ
ÀW
C p
Applying Eq. (63C)
DS ¼
Z B
A
C p
T
dT ¼ C p ln
T A þ
ÀW
C p
T A
[0
ð
Þ
which is positive as long as work is done to the body, i.e., W is negative. A possibility of spontaneous work derived from the body is, of course, impossible in
violation of the entropy principle. Note that a workflow is not associated with an
entropy flow, this increase of entropy is not compensated by an entropy outflow
from (thus, a decrease of entropy in) the system of work source. This increase of
entropy in affected part of the body is the total change of entropy for the “composite
system of body and work-source.”
5.6 The Definition of Heat
The entropy principle holds that all spontaneous transformations in an isolated
system proceed in the direction of increasing entropy, such transformations manifest in either the dispersal of gradients or the dissipation of high-grade energy into
low-grade energy eventually into heat energy. With this understanding, we can
104
5 Entropy and the Entropy Principle