Relation between cp and cvSpecific heat is defined as the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. There are two types of specific heat: Cp and Cv.
CpCp is the specific heat at constant pressure. It is defined as the heat required to raise the temperature of a substance by one degree Celsius at constant pressure. Cp is always greater than Cv.
CvCv is the specific heat at constant volume. It is defined as the heat required to raise the temperature of a substance by one degree Celsius at constant volume. Cv is always less than Cp.
Relation between Cp and CvThe relationship between Cp and Cv can be expressed as:
Cp - Cv = R
where R is the gas constant for a particular gas. This relationship is known as Mayer's formula.
For an ideal gas, the value of R is constant, and hence the difference between Cp and Cv is also constant. The value of R depends on the molar mass of the gas and the universal gas constant.
The value of Cp is always greater than Cv because, during the heating process, some heat energy is used to do work in expanding the gas. This work done is not present in the case of constant volume heating, and hence Cv is always less than Cp.
The relationship between Cp and Cv is essential in thermodynamics as it helps in calculating the change in internal energy and enthalpy of a system.