The ratio of cp/cv for monoatomic gas is?

Question: The ratio of cp/cv for monoatomic gas is?

The ratio of cp/cv for a monoatomic gas is a measure of how much heat is required to raise the temperature of one mole of the gas by one degree Celsius at constant pressure and constant volume. It is also known as the γ-factor or the  adiabatic index. For an ideal monoatomic gas, this ratio is equal to  5/3 or 1.67,

This value can be derived from the  equipartition theorem, which states that any quadratic energy term such as kinetic energy contributes equally to the internal energy of a system in thermal equilibrium. A monoatomic gas has only  three degrees of freedom due to its translational motion, so its internal energy per mole is U = 3/2 RT, where R is the universal gas constant and T is the temperature. The heat capacity at constant volume, cv, is the derivative of the internal energy with respect to the temperature, so cv = 3/2 R. The heat capacity at constant pressure, cp, can be estimated by using the relation cp – cv = R, which is strictly true for an ideal gas and a good approximation for real gases. Therefore, cp = 5/2 R and the ratio cp/cv = 5/3.

The ratio of cp/cv for a monoatomic gas is important for understanding the behavior of gases under different thermodynamic processes. For example, in an isentropic process, which is a reversible adiabatic process (no heat exchange), the pressure and volume of a gas are related by pVγ = constant, where γ is the ratio of cp/cv. This equation can be used to calculate the work done by or on a gas in such a process.