Page 26 - Advanced Thermodynamics for Engineers, Second Edition

10 CHAPTER 1 INTRODUCTION AND REVISION

(b) Work process
In this case the work ðdW s Þ is done on the system is in the form of a paddle wheel stirring the fluid
contained in the system. If the system is insulated from the surroundings, the process is adiabatic and
dQ ¼ 0. Hence, applying the First Law (Eqn (1.18)) gives
dQ ¼ dU þ dW
but in this case, while dQ ¼ 0, the work term, dW, is made up of two components:

• the stirring work, dW s ,
• the pdV work done in raising the weight due to the change in properties of the substance, e.g.
temperature.
Equations (1.18) then becomes
0 ¼ dU þ pdV dW s ; (1.20)
which may be rewritten to give
dW s ¼ dU þ pdV: (1.21)

Since this was a constant pressure process it is possible to write Eqn (1.21) as
dW s ¼ dðU þ pVÞ¼ dH: (1.22)
where H is termed the enthalpy of the system.
If the end states of the two processes are the same, then the heat and work transfer processes are
equivalent. Thus both the heat and work transferred to the system are equal to the change of enthalpy.
Thus Eqn (1.19) can be written
dQ ¼ dH: (1.23)

1.5.7 ENTHALPY, H, AND SPECIFIC ENTHALPY, h
Enthalpy is a property because it is defined as
H ¼ U þ pV; (1.24)
which is the sum of a property, U, and the product of two other properties, pV. The specific enthalpy, h,
of a substance can be defined in a similar way to the specific internal energy, etc. and it is
H U þ pV U pV
h ¼ ¼ ¼ þ ¼ u þ pv: (1.25)
m m m m

1.5.7.1 Specific heat at constant pressure, c p
The specific heat at constant pressure is defined in a similar manner to that at constant volume. It is
defined as the rate of change of specific enthalpy at constant pressure with temperature. The math-
ematical definition of c p is

dh dh dQ
c p ¼ ¼ ¼ (1.26)
dT dt dT
p p p