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This law expresses the link between the 3 fundamental quantities that define the state of a gas: PRESSURE (P), TEMPERATURE (T) and VOLUME (V).
The law is expressed by the formula

PV = nRT (1)

where "n" are the moles of the gas we are considering and "R" is the UNIVERSAL CONSTANT OF GASES whose value is 0.08205, if P is expressed in Atm, T in Kelvin degrees (C + 273.16) and V in litres.

This formula allows us to calculate the 3rd quantity when we know the first two and this is simple, but we can also study the behaviour of a gas when one of them is kept constant.
This is true when the transformation on a date mass of gas is REVERSIBLE, respecting the following conditions:
- The transformation is extremely slow, to allow the gas to be always in equilibrium conditions
- There's no friction in the container of the gas when we vary P in function of V
- There's no heat exchange with the exterior when T remains constant.

At this point, we can have three possible cases:

A) T = CONSTANT
For a date T, we can study the behaviour of P in function of V, varying the volume of the gas into a piston container.
This behaviour follows an hyperbolic curve so that, as V increases, P decreases and, on the contrary, when we reduce the inner V, the gas is compressed and its P increases.
This case is described by the BOYLE equation:

PV = K (2) (where K is a constant including T) or, also

P1*V1 = P2*V2 (3)

B) V = CONSTANT
If we keep constant the V of a certain amount of gas in a rigid container, we can study P in function of T, explaining the well-known fact that a gas, heated in a constant V (always in reversible conditions) increases its P according to the CHARLES LAW:

P/T = K (4) or, also

P1/T1 = P2/T2 (5)

that express a direct proportionality between P and T so that P varies LINEARLY in function of T.

C) P = CONSTANT
In this case, the volume of the container is left free to increase (considering considering negligible the friction and the mass of the piston) when the T of the gas increases.
This is another direct proportionality, this time, between T and V and it's expressed by the GAY-LUSSAC LAW:

T/V = K (6) or, also

T1*V1 = T2*V2 (7)

The perfect gas law is valid for the limit case of an IDEAL GAS that must respect the following conditions:
1) The total volume of gas particles (atoms or molecules) is negligible respect to that of their container so that we can compress the gas until nearly V = 0.

2) The interactions among gas particles are absent so that the chemical nature of the gas is negligible.

3) The

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