Molar specific heat capacity of a substance is _________.

Explanation:

Specific heat capacity: 

• It is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celcius.
• Specific heat capacity (c) is related to the heat (Q) and temperature (T) as follows
• ΔQ = mc ΔT........(1)
• The SI unit of specific heat capacity is J kg-1 K-1

Molar Specific Heat or Molar Heat Capacity

• The molar heat capacity of a substance is defined as the amount of heat required to raise the temperature of one gram mole of the substance by one degree Celsius.
• Its unit is cal.mol^-1°C^-1 or J.mol^-1K^-1
• The molar-specific heat of a substance is generally represented by C.
• If the specific heat of a substance is c and its gram molar mass is M, then
• C = Mc.....(2)
• From equation 1 and 2
• \(Δ Q=\frac{C}{M}m Δ T\)
• ΔQ = μCΔT  
• where, μ = m/M
• \(C=\frac{1}{µ} \frac{ΔQ}{ΔT}\)

• where, µ is the number of moles.

• Molar-specific heat of gas is of two types. This is because the amount of heat required to raise the temperature of one mole of a gas is different when:
  1. heat is supplied at constant pressure C_p and
  2. when heat is supplied at constant volume C_v

(a) Molar specific heat of a gas at constant pressures Cp

• The amount of heat energy required to raise the temperature of one mole of a gas by 1°C constant pressure is called molar specific heat of a gas at constant pressure:

(b) Molar specific heat of a gas at constant volume Cv

• The amount of heat energy required to raise the temperature of one mole of a gas by 1°C at constant volume is called molar specific heat of a gas at constant volume.