Ideal Gases in Isobaric Processes

Definition: Isobaric Process

An isobaric process is a process in which the pressure of the gas remains constant.

Theorem: Work in an Isobaric Process

The work $W$ which an ideal gas does during an isobaric process depends on its pressure $p$ and the change $\Delta V$ in its volume:

$$W=p\Delta V$$

PROOF

Let $V_i$ and $V_f$ denote the initial and the final volume of the gas,Since $p$ is constant and does not depend on the volume, this theorem gives us

$${\int }_{V_i}^{V_f}p\mathrm{dV}=pV{|}_{V_i}^{V_f}=p{V}_f-p{V}_i=p(V_f-V_i)=p\Delta V$$

Theorem: Molar Heat Capacity in an Isobaric Process (Mayer's)

The molar heat capacity of an ideal gas in an isobaric processes is denoted as $C_p$ and is

$$C_p=\left(\frac{f+2}{2}\right)R,$$

where $f$ is the number of degrees of freedom of a single gas particle and $R$ is the molar gas constant.

PROOF

TODO