Specific Heat at Constant Pressure

Specific heat at constant pressure is defined as the amount of heat required to raise the temperature of one unit mass of a substance by one degree Celsius while keeping the pressure constant. It is denoted by Cp and expressed in J/kg.K.

The specific heat at constant pressure depends on the nature of the gas molecule. The gas molecule that has the maximum specific heat at constant pressure is oxygen.

Explanation

The specific heat at constant pressure of a gas is related to the number of atoms in its molecule and the degree of freedom of the atoms. Oxygen molecule consists of two atoms, and each atom has five degrees of freedom. Therefore, the oxygen molecule has ten degrees of freedom. The number of degrees of freedom is related to the specific heat of the gas at constant pressure by the following equation:

Cp = (f/2)R

Where Cp is the specific heat at constant pressure, f is the number of degrees of freedom, and R is the gas constant.

For oxygen gas, f = 10, and R = 8.314 J/mol.K. Therefore,

Cp = (10/2)8.314 = 41.57 J/mol.K

In comparison, the specific heat at constant pressure of argon, helium, and nitrogen gases are 20.8 J/mol.K, 20.8 J/mol.K, and 29.1 J/mol.K, respectively. Therefore, oxygen has the highest specific heat at constant pressure among these gases.

Conclusion

In conclusion, oxygen gas has the maximum specific heat at constant pressure among argon, helium, nitrogen, and oxygen gases. The specific heat at constant pressure depends on the number of atoms and the degrees of freedom of the gas molecule.