Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

volume. Likewise,cpcan be defined as the change in the enthalpy of a sub-

stance per unit change in temperature at constant pressure. In other words,

cvis a measure of the variation of internal energy of a substance with tem-

perature, and cpis a measure of the variation of enthalpy of a substance with

temperature.

Both the internal energy and enthalpy of a substance can be changed

by the transfer of energyin any form, with heat being only one of them.

Therefore, the term specific energyis probably more appropriate than the

term specific heat, which implies that energy is transferred (and stored) in

the form of heat.

A common unit for specific heats is kJ/kg · °C or kJ/kg · K. Notice that

these two units are identicalsince T(°C) 
T(K), and 1°C change in

temperature is equivalent to a change of 1 K. The specific heats are some-

times given on a molar basis. They are then denoted by c–vand c–pand have

the unit kJ/kmol · °C or kJ/kmol · K.

4–4 
 INTERNAL ENERGY, ENTHALPY,

AND SPECIFIC HEATS OF IDEAL GASES

We defined an ideal gas as a gas whose temperature, pressure, and specific

volume are related by

It has been demonstrated mathematically (Chap. 12) and experimentally

(Joule, 1843) that for an ideal gas the internal energy is a function of the

temperature only. That is,

(4 –21)

In his classical experiment, Joule submerged two tanks connected with a

pipe and a valve in a water bath, as shown in Fig. 4 –22. Initially, one tank

contained air at a high pressure and the other tank was evacuated. When

thermal equilibrium was attained, he opened the valve to let air pass from

one tank to the other until the pressures equalized. Joule observed no

change in the temperature of the water bath and assumed that no heat was

transferred to or from the air. Since there was also no work done, he con-

cluded that the internal energy of the air did not change even though the

volume and the pressure changed. Therefore, he reasoned, the internal

energy is a function of temperature only and not a function of pressure or

specific volume. (Joule later showed that for gases that deviate significantly

from ideal-gas behavior, the internal energy is not a function of temperature

alone.)

Using the definition of enthalpy and the equation of state of an ideal gas,

we have

Since Ris constant and u
u(T), it follows that the enthalpy of an ideal gas

is also a function of temperature only:

h
h 1 T 2 (4 –22)

h
uPv

Pv
RT

f¬h
uRT

u
u 1 T 2

Pv
RT

180 | Thermodynamics

AIR

(high pressure)

Evacuated

WATER

Thermometer

FIGURE 4 –22

Schematic of the experimental

apparatus used by Joule.

300 301 K

AIR

m = 1 kg

←

0.718 kJ 0.855 kJ

AIR

m = 1 kg

1000 1001 K←

FIGURE 4 –21

The specific heat of a substance
changes with temperature.

SEE TUTORIAL CH. 4, SEC. 4 ON THE DVD.

INTERACTIVE

TUTORIAL