Question

Explain why $C_p$ is greater than $C_v$ ?

Answer 1

A chemical substance's molar heat capacity is the amount of energy that must be given to one mole of the material in the form of heat to induce a one-unit increase in temperature. It is also the specific heat capacity of the material times its molar mass, or the heat capacity of a sample of the substance divided by the amount of substance in the sample. The joule per kelvin per mole, or $J{K^{ - 1}}mo{l^{ - 1}}$, is the SI unit for specific heat.

Complete answer:
${C_v}$ is the molar specific heat potential of a gas at constant volume, which is the amount of heat required to raise the temperature of one mole of gas by one degree Celsius at constant volume.

${C_p}$ is the molar specific heat potential of a gas at constant pressure, which is the amount of heat required to raise the temperature of one mole of gas by one degree Celsius at constant pressure.

Because the gas is heated at a consistent rate, the heat is simply given to raise the temperature of the gas.As we heat the gas under constant pressure, the amount of gas in addition to the temperature of the gas increases. As the gas expands, it does some additional effort to enhance the volume. As a result, in this example, heat is provided to
1. Raise the temperature of the gas.
2. Complete the mechanical expansion operation.

When a gas is heated at a constant volume, the work performed on it increases the system's internal energy. When a gas is heated under constant pressure, work is done to overcome the pressure, and the volume expands, resulting in a rise in the system's internal energy. As a result, ${C_p}$ might be stated to be higher than ${C_v}$.

Note: The molar heat capacity of a substance, particularly a gas, can be substantially larger when the sample is allowed to expand while it is heated (at constant pressure, or isobaric) than when it is heated in a closed vessel that inhibits expansion, similar to the specific heat (at constant volume, or isochoric). However, the heat capacity ratio derived from the matching specific heat capacities is the same for both.