Molar heat capacity at constant volume

Definition

Molar heat capacity at constant volume ($C_V$) is the amount of heat required to raise the temperature of one mole of a substance by 1 degree Celsius at constant volume. It is a key parameter in understanding the thermodynamic properties of gases.

5 Must Know Facts For Your Next Test

1. $C_V$ for an ideal monatomic gas is $\frac{3}{2}R$, where $R$ is the universal gas constant.
2. For diatomic gases, $C_V$ can be approximated as $\frac{5}{2}R$ at room temperature due to rotational degrees of freedom.
3. $C_V$ remains constant for an ideal gas but varies for real gases with changes in temperature and pressure.
4. $C_V$ is related to internal energy change: $\Delta U = n C_V \Delta T$, where $n$ is the number of moles and $\Delta T$ is the change in temperature.
5. In thermodynamics, knowing $C_V$ helps predict how a gas will respond to energy added or removed under constant volume conditions.

Review Questions

• What is the molar heat capacity at constant volume ($C_V$) for an ideal monatomic gas?
• How does the molar heat capacity at constant volume differ between monatomic and diatomic gases?
• Why is it important to consider whether conditions are at constant volume when discussing molar heat capacity?

Related terms

Molar Heat Capacity at Constant Pressure ($C_P$): The amount of heat required to raise the temperature of one mole of a substance by 1 degree Celsius at constant pressure.

Universal Gas Constant ($R$): A physical constant that appears in many fundamental equations in thermodynamics, with a value approximately equal to $8.314 \, J/(mol \cdot K)$.

Internal Energy ($U$): The total energy contained within a system due to both kinetic and potential energies of its molecules.