Question

I've come across this article which says that the constant pressure heat capacity is independent of pressure.

It also gives a mathematical explanation which says that any work of an ideal gas at constant pressure heating is equal to -R for all pressures. How can one rationalize this, because I am having trouble understanding why this needs to be the case.
And also, how can one account for the pressure dependence using a real gas equation?

Answer 1

The constant pressure heat capacity, Cp, of an ideal gas is independent of pressure because the work done during heating is equal to -R. The pressure dependence can be accounted for in a real gas using equations such as the van der Waals equation.

Step-by-step explanation:

The constant pressure heat capacity, Cp, of an ideal gas is independent of pressure. This is because at constant pressure, the work done by an ideal gas during heating is equal to -R, where R is the ideal gas constant.

The mathematical explanation for this is derived from the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

For a real gas, the pressure dependence can be accounted for using a real gas equation, such as the van der Waals equation:

(P + (an^2/V^2))(V - nb) = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and a and b are constants that depend on the gas. This equation takes into account the attractive forces between gas molecules (represented by the term an^2/V^2) and the volume occupied by the gas molecules (represented by the term nb).