Specific heats of a gas | Types | Formula

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Definition of specific heat:


The amount of heat per unit mass required to raise the temperature by one degree Celcius is called specific heat. It is denoted as c. All the solids and liquids have only one specific heat and gas can have any number of specific heat depending upon conditions, under which it is heated. 

Types of specific heat:

  1. Specific heat at constant volume 
  2. Specific heat at constant pressure

Specific heat at constant volume:


The amount of heat required to raise the temperature of a unit mass of gas by one degree Celcius is called specific heat at constant volume. It is denoted by Cv. 

Formula:


The total heat supplied to the gas at constant volume is given below. 

 Q = Mass × Rise in temperature × Specific heat at constant volume

 Q = m ×(T2 - T1) × Cv 

 Where m = mass of the gas

T1 = Initial temperature of the gas
T2 = Final temperature of the gas

 When specific heat at constant volume Cv is multiplied by the molecular mass of a gas is called volumetric or molar specific heat at constant volume denoted as Cvm.

 Cvm = M × Cv

Specific heat at constant pressure:


The amount of heat required to raise the temperature of a unit mass of gas by one degree Celcius is called specific heat at constant pressure. It is denoted by Cp. 

Formula:

The total heat supplied to the gas at constant pressure is given below. 

Q = Mass × Rise in temperature × Specific heat at constant pressure

 Q = m ×(T2 - T1) × Cp

 Where m = mass of the gas

T1 = Initial temperature of the gas
T2 = Final temperature of the gas

 When specific heat at constant volume Cp is multiplied by the molecular mass of a gas is called volumetric or molar specific heat at constant volume denoted as Cpm.

 Cpm = M × Cp 

 Notes: 

 At constant pressure, the specific heat is higher than the specific heat at constant volume.

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