Question

What is Mayer’s formula?

Answer 1

Hint: Mayer's formula is an important thermodynamic relationship associated with heat capacities of gases. Heat capacity in itself is an extensive quantity but when molar or specific heat capacity is calculated, it becomes an intensive quantity.

Complete answer:
Heat capacity is an important thermodynamic property that gives the measure of amount of heat needed to bring about a unit rise in temperature of the system under observation.
Molar heat capacity is heat capacity measured per mole of a substance and is an intensive quantity unlike heat capacity which is an extensive property.
Heat in itself is a path function and shows different values when calculated differently.
Though the heat capacity for a particular substance is fixed, it depends upon the conditions under which it is measured. The heat capacity measured at constant pressure is different from the heat capacity measured at constant volume, especially in the case of gases. The heat capacity at constant pressure is always greater than that measured at constant volume for any particular gas.
Mayer’s formula relates the difference between the heat capacities at constant pressure and volume with the universal gas constant. The formula can be written as follows:
\[{C_p} - {C_v} = R\]
Where, \[{C_p} = \] molar heat capacity measured at constant pressure
\[{C_v} = \] molar heat capacity measured at constant volume
And \[R = \] the universal gas constant
When heat capacities are taken instead of molar heat capacities than the relation becomes as follow:
\[{C_p} - {C_v} = nR\]
This relationship can be derived using the formulas of enthalpy and internal energy at constant pressure and volume respectively.

Note:
The relation between molar heat capacities and gas constant given by Mayer’s formula holds true for an ideal gas (or gases behaving as ideal gases at high pressure and low temperature conditions) only. Real gases have a different formula that accommodates van der Waals constants taking into account the intermolecular forces of attraction.