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§2 Mendeleev-Clapeyron equation

Every system can be in different states with different temperature, pressure, volume, etc.

The values ??of p, V, T, and others characterize the state of the system, called the parameters of the state.

If any of the parameters within the system varies from point to point, a condition called non-equilibrium. If the system parameters are the same at all points under constant external conditions, such a state is called equilibrium.

Any process, ie transition from one state to another is related to an imbalance of the system. But infinitely slow process will consist of a sequence of equilibrium states. This process is called equilibrium. At sufficiently low flow real processes can approach to equilibrium. Equilibrium process is reversible, that is, the system goes from state 1 to state 2 and from 2 - 1, passing through the same intermediate states.

The process by which the system, having a number of intermediate states, returns to its original state is a round or cycle process: the process of 1-2-3-4-1 in the figure.

Relationship between the parameters of the state called the state equation:

 f (p, V, T) = 0

Clapeyron, using the laws of Boyle and Charles led the ideal gas equation.

1 – 1’: T = const – Boyle-Mariotte law:

 p1V1 = p1’ V2;

1’ – 2: V = const – Charles law


because states 1 and 2 are chosen arbitrarily, for a given mass of gas quantity  is constant

 - Clapeyron equation

B - gas constant, is different for different gases.

Mendeleev Clapeyron equation combined with the law of Avogadro

 - for 1 mole

Vmmolar volume

Mendeleev-Clapeyron equation

R - universal (molar) gas constant

p = const;  :

The physical meaning of R: is numerically equal to the work done by the gas during the isobaric (p = const) heating one mole of gas (m / μ = ν = 1) by one Kelvin (ΔT = 1 K)
We introduce the Boltzmann constant


p - pressure of an ideal gas at a given temperature is directly proportional to the concentration of the molecules (or gas density). At the same p and T, all gases contain in unit volume the same number of molecules.

n - concentration of molecules (number of molecules per unit volume). The number of molecules under normal conditions in 1 m3 called the number Loschmidt:

§ 3 The basic equation of the molecular-kinetic theory (m.k.t.) gases.

At random motions of gas particles collide with each other and with the walls of the vessel. The mechanical action of the collision, the vessel is seen as pressure on the walls. We distinguish on wall of the vessel some elementary area ΔS and find the pressure on this area.
The momentum obtained by concerned wall by the impact of a single molecule will be equal

m0 - mass of a single molecule.

 Newton's second law can be written as:

Δti-time between two successive collisions of the i-th molecule with this wall

All directions are equivalent:

We introduce the mean square velocity, which characterizes the whole set of molecules


 - the basic equation of the MKT

From equation Mendeleev - Clapeyron:

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