**Specific heat** is a property related to** internal energy** that is very important in thermodynamics. The **intensive properties c_{v}** and

*are defined for pure, simple compressible substances as partial derivatives of the*

**c**_{p}**internal energy**and

*u(T, v)***enthalpy**, respectively:

*h(T, p)*where the subscripts **v** and **p** denote the variables held fixed during differentiation. The properties **c _{v} **and

**c**are referred to as

_{p}**specific heats**(or

**heat capacities**). Under certain special conditions, they relate the temperature change of a system to the amount of energy added by heat transfer. Their SI units are

**J/kg K,**or

**J/mol K**. Two specific heats are defined for gases,

**constant volume (c**and

_{v}),**constant pressure (c**.

_{p})According to the **first law of thermodynamics**, for a constant volume process with a monatomic ideal gas, the molar specific heat will be:

*C _{v} = 3/2R = 12.5 J/mol K*

because

*U = 3/2nRT*

It can be derived that the **molar specific heat** at constant pressure is:

**C _{p} = C_{v} + R = 5/2R = 20.8 J/mol K**

This ** C_{p}** is greater than the molar specific heat at constant volume

**because energy must now be supplied**

*C*_{v}**not only**to

**raise the temperature**of the gas but also for the

**gas to do work**because, in this case, volume changes.