Ideal Gas

In an ideal gas, molecules are spaced far enough apart that intermolecular forces are negligible.

Ideal Gas Law

Original form:

$$PV=nR°T$$

where $R°=8.314\left[\frac{\text{kJ}}{\text{kmol}\cdot \text{K}}\right]$.

Alternative form:

$$PV=mRT$$

where $R=\frac{R°}{M}\left[\frac{\text{kJ}}{\text{kg}\cdot \text{K}}\right]$.

Specific volume form:

$$Pv=RT$$

For an ideal gas, there is no latent energy stored in intermolecular bonds.

• As such, internal energy is due entirely to sensible energy from molecular motion (translation, rotation, vibration).
• In other words, internal energy is a function only of temperature $u=u(T)$

Ideal Gas Assumptions

Real gas approximates ideal gas when it is dilute.

• Low density (large specific volume)
• Low $P$ and high $T$

With respect to the critical point, the assumption is valid when:

• $P\ll P_{cr}$
• $T\gg T_{cr}$