Molar Specific Heat

Amount of heat energy required to raise the temperature of one mole of a substance by one kelvin is called molar specific heat.
It is denoted by “Cn“
Mathematically,
D Q = n Cn DT
Where n = number of moles of substance
Or
Cn = DQ /n DT

Unit Of Molar Specific Heat
J/mole K OR J mole-1 K-1.

Molar specific heat of gases
Gases have two types of Molar specific heat because it depends whether the gas is allowed to expand or not when heated .
When the volume of the gas is kept constant, its specific heat is called “molar specific heat at constant volume”.
When the pressure of the gas is kept constant, its specific heat is called molar specific heat at constant pressure.

Molar specific heat at constant volume
“Amount of heat energy required to raise the temperature to one mole of a gas by one kelvin at constant volume is called molar specific heat at constant volume”.
It is denoted by Cv.

Mathematical expression
D Qv = n Cv D T
Or
Cv = D Qv /n D T
Unit:
J/ mole K or J/ mole-1 K-1
At constant volume all the heat supplied is fully utilized in increasing the temperature of the gas.