Physical Chemistry , 1st ed.

other hand, if heat comes out of a system,qis negative. The sign on qthere-

fore tells one the direction of the heat transfer.

The same change in temperature requires a different amount of heat for dif-

ferent materials. For example, a system composed of 10 cm^3 of iron metal gets

hotter with less heat than does 10 cm^3 of water. In fact, the amount of heat

necessary to change the temperature is proportional to the magnitude of the

temperature change,T, and the mass of the system m:

q m T

In order to convert a proportionality to an equality, a proportionality constant

is needed. For the above expression, the proportionality constant is represented

by the letter c(sometimes s) and is called the specific heat(or specific heat

capacity):

qmcT (2.9)

The specific heat is an intensive characteristic of the material composing the

system. Materials with a low specific heat, like many metals, need little heat

for a relatively large change in temperature. Table 2.1 lists some specific heats

for selected materials. Units for specific heat are (energy)/(masstemperature) or

(energy)/(molestemperature), so although the SI units for specific heat are

J/gK or J/molK, it is not unusual to see specific heats having units of

cal/mol°C or some other set of units. Notice that, because equation 2.9 in-

volves the changein temperature, it does not matter if the temperature has

units of kelvins or degrees Celsius.

Heat capacity Cis an extensive property that includes the amount of mate-

rial in the system, so equation 2.9 would be written as

qCT

Example 2.4

a.Assuming that 400. J of energy is put into 7.50 g of iron, what will be the

change in temperature? Use c0.450 J/gK.

b.If the initial temperature of the iron is 65.0°C, what is the final tempera-

ture?

Solution

a.Using equation 2.9:

400. J (7.50 g)(0.450 J/gK)T
     Solving for T:
     T
     118 K
     The temperature increases by 118 K, which is equal to a temperature change
     of 118°C.
     b.With an initial temperature of 65.0°C, an increase of 118°C brings the sam-
     ple to 183°C.

Example 2.5

With reference to Joule’s apparatus in Figure 2.6, assume that a 40.0-kg

weight (which experiences a force due to gravity of 392 newtons) falls a dis-

tance of 2.00 meters. The paddles immersed in the water transfer the decrease

2.2 Work and Heat 31

Table 2.1 Specific heat capacities of
various materials
Material c(J/gK)
Al 0.900
Al 2 O 3 1.275
C 2 H 5 OH, ethanol 2.42
C 6 H 6 , benzene (vapors) 1.05
C 6 H 14 ,n-hexane 1.65
Cu 0.385
Fe 0.452
Fe 2 O 3 0.651
H 2 (g) 14.304
H 2 O (s) 2.06
H 2 O (), 25°C 4.184
H 2 O (g), 25°C 1.864
H 2 O, steam, 100°C 2.04
Hg 0.138
NaCl 0.864
O 2 (g) 0.918