# Heat Capacity

We have studied about the exchange of heat between system and surrounding. Now, we s hall focus on the measurement of heat. The heat transferred to the system appears as a rise of its temperature. The increase of temperature ( ΔT) is directly proportional to the quantity of heat (q) absorbed by the system. It can be put as

q = ΔT = or q = C.T

where C is called heat capacity of the system the value of which depends upon the size, composition and nature of the system.

Now, if the temperature difference (.1T) is unity, i. e., l0 celsius or 1° kelvin then, q = C. Thus, heat capacity of the system is defined as the quantity of heat required to raise its temperature through ] 0.

Equation (16.1) reveals that a given amount of heat will raise the temperature of the system to a smaller extent if its heat capacity is large and vice versa.

MOLAR HEAT CAPACITY

The molar heat capacity of a substance (Cm) is the heat required to raise the temperature of 1 mol of the system through 1°. If C is the heat capacity of n mol of system then its molar

heat capacity, Cm is given by

C m = Heat capacity / Number of moles = C / n

SPECIFIC HEAT CAPACITY (c)

This term is used more frequently for solids and liquids. We know beat capacity of a system depends upon the quantity of matter in the system. For example, large block of aluminium has a higher heat capacity than does a small piece of the same metal. Specific heat capacity (c) is a heat capacity of 1 g of the sample. It is the quantity of heat required to raise the temperature of 1 gram of substance through 1 K (or JOC).

Specific heat capacity ( c) = Heat capacity / mass = C/m

Now , C = q / ΔT

• Specific heat capacity of water

= 4.184 kJ kg-1K-1 or 4.184 Jg-1K-1

Specific heat capacity (c) = q / mΔT

or                     q = c x m x ΔT

Units of specific heat capacity are:

Jg-1 K-1 or Jg-1 (0C-1)

The specific heat capacity (c) and molar heat capacity (Cm) of the substance are related as

C x molar mass = Cm