# UY1: Heat Capacity

The heat capacity (C) of a body is the amount of heat required to raise the temperature of that body by one degree of temperature.

If the heat capacity varies with temperature, we can define heat capacity as the ratio of the infinitesimal heat flow (dQ) to the infinitesimal temperature change (dT).

$$C = \frac{d Q}{d T}$$
A unit of heat capacity is J/°C. Heat capacity is an extensive property, i.e., it depends on the size of the body.

The specific heat or specific heat capacity (c) of a substance is the heat capacity per unit mass.

$$c = \frac{1}{m} \frac{dQ}{dT}$$
A unit of specific heat capacity is  J/°C. Specific heat capacity is an intensive property, i.e, it does not depend on the size of the body.

The specific heat capacity of materials vary with temperature (and for gases, also with pressure). When this variation may not be neglected, the amount of heat required to change the temperature of the body from T1 to T2 can be obtained by integration.

$$Q = m \, \int\limits_{T_{1}}^{T_{2}} c \, dT$$

If the variation can be neglected, the integral simplifies to:

$$Q = mc (T_{2} – T_{1})$$

### Latent Heat

The latent heat (L) for a phase transition of a substance is the amount of heat required to cause the stated phase transition per unit mass of the substance. Hence, the heat flow associated with the phase transformation of a mass (m) is,

$$Q = mL$$

Type of phase transformations:
a) Melting (fusion): Solid to liquid
b) Vaporization: Liquid to vapour
c) Sublimation: Solid to vapour and their reverse processes.

The energy absorbed or released by the substance as latent heat during phase transition does not result in any temperature change (hence the heat is “latent” or “hidden”). The energy is stored as potential energy in breaking the bonds between molecules. It is also related to the entropy of the phase transition.

Latent heat of transformation is also known as enthalpy of transformation (ΔH) and given in per mol of the substance.

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