What is the equation for heat capacity at constant pressure (Cp) for a monoatomic gas?

The heat capacity at constant pressure ((C_p)) for a monoatomic ideal gas is indeed given by the equation (C_p = \frac{5}{2}R). This result is derived from the principles of thermodynamics and kinetic theory.

For an ideal monoatomic gas, the internal energy ((U)) is primarily due to the kinetic energy of the gas particles. Each degree of freedom contributes (\frac{1}{2}R) to the internal energy per mole of gas. A monoatomic gas has three translational degrees of freedom, which means the internal energy can be expressed as:

[

U = \frac{3}{2}RT

]

At constant pressure, the relationship between heat capacity at constant volume ((C_v)) and heat capacity at constant pressure is given by:

[

C_p = C_v + R

]

With a monoatomic gas, the heat capacity at constant volume ((C_v)) is given by:

[

C_v = \frac{3}{2}R

]

Substituting this into the equation for (C_p):

[

C_p = \frac{3}{2}R + R = \frac