What is Molar Heat Capacity?

Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one kelvin (or one degree Celsius).

SI Unit: J mol-1 K-1

Formula

Molar heat capacity (Cm) is given by:

Cm = Q / (n ΔT)

• Q = heat supplied
• n = number of moles
• ΔT = change in temperature

Types of Molar Heat Capacity

Molar Heat Capacity at Constant Volume (Cv)

Heat required to raise the temperature by 1 K while volume remains constant. No boundary work is done.

Molar Heat Capacity at Constant Pressure (Cp)

Heat required to raise the temperature by 1 K while pressure remains constant. The system does expansion work.

General relation: Cp > Cv

Example (Ideal Monoatomic Gas)

For an ideal monoatomic gas:

• Cv = (3/2) R
• Cp = (5/2) R

Here, R is the universal gas constant.