The Ideal Gas

Contents

• Definition
• Summary of properties
• About this document ...

Definition

Definition of ideal gas.
The ideal gas is a system in which there are no intermolecular interactions.

All properties of the ideal gas may be derived from this simple definition. In mechanical terms, the ideal gas has no potential energy, only the kinetic energy due to the motions of its atoms.

Ideal gas equation of state
The ideal gas obeys the following equation of state

$$pV =  nRT$$

where p - pressure, V - volume, n - amount of substance, T - temperature and R = 8.314 $\frac{J}{mol K}$ is the universal gas constant.

The equation of state may be derived theoretically from the definition of the ideal gas above. This equation is often used as an alternative definition of a model substance called the ideal gas. No real substance behaves like an ideal gas over the full range of (p,T). Real gases approximately follow the ideal gas equation of state under conditions when their intermolecular interactions may be neglected, i.e. at sufficiently low pressures. The ideal gas (IG) is an important model for illustrating concepts of thermodynamics.

Summary of properties

Equation of state.

$$pV = nRT$$

Energy.

The energy of the ideal gas depends on T only, not on p or V. For any process involving the ideal gas

$$\Delta U =  C_V \Delta T$$

Enthalpy.

The enthalpy of the ideal gas depends on T only, not on p or V. For any process involving the ideal gas

$$\Delta H =  C_P \Delta T$$

Heat capacities.

The two heat capacities of an ideal gas are related. For any kind of ideal gas

$$C_P =  C_V +  nR    or      C_{P,m} =  C_{V,m} +  R$$

For the special case of the mono-atomic ideal gas we know the value of $C_V$ and we can use the relation above to calculate $C_P$

$$C_{V,m} =  \frac{3}{2}R     C_{P,m} =  \frac{5}{2}R     (mono-atomic IG)$$

See Kinetic Theory of Gases for derivation.

About this document ...

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The translation was initiated by KK on 2003-09-10