The molar heat capacity for an ideal monoatomic gas is the amount of heat energy required to raise the temperature of one mole of gas by one degree Kelvin (or Celsius) at constant volume. It is denoted by the symbol Cv and has a value of 3R/2, where R is the gas constant.
Molar heat capacity for an ideal monoatomic gas differs from other types of heat capacity because it only takes into account the internal energy of the gas molecules. This means that it does not include any energy associated with the motion or rotation of the gas molecules.
For an ideal monoatomic gas, the molar heat capacity is independent of temperature. This means that the amount of heat energy required to raise the temperature of the gas by one degree remains constant, regardless of the initial temperature of the gas.
The molar heat capacity of an ideal monoatomic gas is generally lower than that of a real gas. This is because real gases have additional degrees of freedom, such as molecular rotation and vibration, which require additional energy to raise their temperature.
The molar heat capacity of an ideal monoatomic gas is affected by the number of gas molecules present, the type of gas, and the temperature. It is also dependent on the type of process (constant volume or constant pressure) and the presence of any external energy sources, such as heat transfer or work done on the gas.