Heat Capacity: Definition and Explanation

The physical and chemical changes are usually accompanied by energy changes. While studying heat engines and the concepts related to heat, scientists and mechanical engineers established a quantitative relationship between heat and mechanical energy which gave rise to a new branch of science, known as Thermodynamics (thermo: heat, dynamics: movement).

In modern thermodynamics, heat is defined as the measure of the total internal energy of a system, this includes the total kinetic energy of the system and the potential energy of the molecules present in the system. The system’s internal energy is found to increase with a rise in temperature, this rise in internal energy is dependent on the temperature difference, the amount of matter, etc. In order to quantify the heat energy associated with matter and its dependence on temperature, two properties were defined and these properties were named as Heat Capacity and Specific Heat Capacity of the system.

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Heat Capacity

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Heat Capacity or Thermal Capacity refers to the physical property of a matter. It can be defined as the amount of heat to be supplied to an object in order to produce a unit change in its temperature. SI Unit of the Heat Capacity is Joule per Kelvin. It is denoted by C.

Where, ΔQ is the amount of heat that must be given to the object (of mass M) so that it raises its temperature by ΔT. 

Heat Capacity of an object depends on the initial temperature T of the object and the pressure P applied to it. Hence, Heat Capacity (C) can be considered as a function C (P, T) of these two variables, temperature and pressure.

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We can also define heat capacity as the quantity of heat that is required to increase the temperature of the system by one degree Celsius (or one Kelvin). Heat Capacity is an extensive characteristic of the matter.

1. Extensive Properties: The properties which depend upon the quantity of matter present in the system are called extensive properties. For example, number of moles, mass, volume, enthalpy, heat capacity, entropy, free energy, etc. 
2. Intensive Properties: The properties which do not depend upon the quantity of matter present in the system are called intensive properties. For example, temperature, density, concentration, specific heat capacity, viscosity, surface tension, etc.

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Specific Heat Capacity 

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The quantity that does not depend on the quantity or size of matter under consideration for thermodynamic studies, made the scientists define specific heat capacity. It can be referred to as an intensive property as it is independent of the quantity or size of the matter. The Specific Heat Capacity of a system is the amount of heat required to raise the temperature of the unit mass of the substance (present in the system) by one degree Celsius (or one Kelvin). Specific Heat Capacity is denoted by c. 

\(c = \frac {C}{M} = \frac{1}{M} . \frac{dQ}{dT}\)

Where, dQ represents the amount of heat required to uniformly raise the temperature of the sample substance by an infinitesimally small increment in temperature dT.

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Molar Heat Capacity

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The Molar Heat Capacity of a system can be referred to as the amount of heat required to increase the temperature of a single mole of the substance ( in the system) by one Kelvin. The Molar Heat Capacity of a system is denoted by c_m. And it is equal to

where ΔQ is the amount of heat required to raise the temperature of the sample by ΔT. It is certain that this parameter cannot be utilised to compute when n is not known or defined. 

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For a system, particularly for a gaseous system, the heat capacity measured at constant volume is quite different from that measured at constant pressure. Hence, molar heat capacity is of following two types: 

1. Molar heat capacity at constant volume (C_v) 
2. Molar heat capacity at constant pressure (C_p) 

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Relationship between C_p and C_v

When the volume of a system is kept fixed and heat is added to the system, then the system will not be able to work. The system uses the complete heat that it has absorbed to increase the internal energy of the system.

If the pressure present in the system is kept fixed and heat is provided to the system, then certain work of expansion is done by the system in addition to the rise in the internal energy.

If at a fixed pressure the temperature of the system is needed to be raised through the same values at a fixed volume, then for the expansion work some extra heat needs to be applied. Therefore C_p > C_v.

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Things to Remember

• The physical and chemical changes are usually accompanied by energy changes.
• While studying heat engines and the concepts related to heat, scientists and mechanical engineers established a quantitative relationship between heat and mechanical energy which gave rise to a new branch of science, known as Thermodynamics.
• Heat Capacity or Thermal Capacity refers to the physical property of a matter. It can be defined as the amount of heat to be supplied to an object in order to produce a unit change in its temperature.
• SI Unit of the Heat Capacity is Joule per Kelvin.
• The Molar Heat Capacity of a system can be referred to as the amount of heat required to increase the temperature of a single mole of the substance ( in the system) by one Kelvin.
• If the pressure present in the system is kept fixed and heat is provided to the system, then certain work of expansion is done by the system in addition to the rise in the internal energy.

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