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For a given value of T, the quantity of the heat absorbed also depends upon the mass
m of the body. The greater is the mass, the greater the quantity of heat absorbed. For
example, if we heat 50 grams of water through 10C, and 100 grams of water also
through 10C, then the quantity of heat absorbed by 100 gms of water will be twice the
quantity of heat absorbed by 50 gms of water. In other words, the quantity of heat
absorbed is directly proportional to mass. Thus, we have the relation:

Q = f(m) (1.31)

Combining two relations, we get :

Q = f(T, m) or Q = C m T, (1.32)
where C is a constant, which depends upon the material of the body.

C - called the specific heat of the body. If m  1 kg ; T  1 K , then Q  C by the
equation (1.32).
Thus the specific heat of a substance is the amount of heat required to change
temperature of one unit quantity of substance through 1K.
Neither the heat capacity of a body nor the specific heat of a material is constant but
depends on the location of the temperature interval. At ordinary temperatures and over
ordinary temperature intervals, however, specific heats can be considered to be

constants. For example, the specific heat of water varied less then 1% from its value
of 4.19 kJoule over the temperature range from 0C to 100C. If we calculate specific
kg  K
heat in some temperature interval we get average specific heat :

t 2 q x
C xm  . (1.33)
t
1 t 

For the very small interval of the temperature we get true specific heat:

q dqx
C  lim x  . (1.34)
x
 T dt

What we gained by this specific heat also depends on character of thermodynamic
process. When a gas is heated at constant volume, the quantity of heat required to raise

the temperature of unit mass of the gas through 1C is called its specific heat at constant
volume, and is denoted by C . When a gas is heated at constant pressure, the quantity of
v
heat required to raise the temperature of unit mass of the gas through 1°C is called its
specific heat at constant pressure, and is denoted by C p.
It can be shown that C p > C v. When a gas is heated at constant volume, no work is
done by the gas against any external resistance. In this case, the heat supplied to the gas
is used only in raising the temperature of the gas. But when we heat a gas at constant
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