Question

How do you calculate ${\mathrm{C}}_{\mathrm{p}}$ and ${\mathrm{C}}_{\mathrm{v}}$ for gas mixture?

Answer 1

• At constant volume when the gas is heated, the pressure on gas increases.
• To make the volume constant in a container, put a barricade on the piston. The applied heat, in this case, is used to raise the temperature of $1\mathrm{mole}$ of gas by $1\mathrm{K}$.
• Therefore, ${\mathrm{C}}_{\mathrm{v}}$ is defined as the heat required to raise the temperature of $1\mathrm{kg}$ of a substance (solid, liquid or gas) at constant volume by $1°\mathrm{C}$. Its units are $\mathrm{kJ}/\mathrm{kg}$$°C$.
• Similarly, at constant pressure, when the gas is heated, it expands, here the work is done by the gas. Because the gas does the work to move the piston, the temperature of the gas decreases.
• The relation between ${\mathrm{C}}_{\mathrm{p}}$ and ${\mathrm{C}}_{\mathrm{v}}$ is described as ${\mathrm{C}}_{\mathrm{p}}-{\mathrm{C}}_{\mathrm{v}}=\mathrm{R}$
• Therefore,${\mathrm{C}}_{\mathrm{p}}$ is defined as the amount of heat energy released or absorbed by a unit mass of the substance with the change in temperature at a constant pressure.