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# The gas laws: Boyle's law and Charle's Law

Robert Boyle in 1662, studied the effect of change of pressure on the volume of a given mass of gas at constant temperature. According to Boyle's law, for given mass of a gas at constant temperature, the pressure (P) is inversely proportional to its volume (V).

The gas laws

Boyle's law

Robert Boyle in 1662, studied the effect of change of pressure on the volume of a given mass of gas at constant temperature. According to Boyle's law, for given mass of a gas at constant temperature, the pressure (P) is inversely proportional to its volume (V).

P a 1 / V

(at constant temperature)

V

(or)

PV =      constant.

Thus if V1 is the volume occupied by a given mass of a gas at pressure P1 and V2 is the volume when pressure changes to P2, then as the temperature remains constant, according to Boyle's law

P1 V1         =       P2 V2         =       Constant

Charle's Law

The variation in the volume of a gas with temperature at constant pressure is given by charle's law. The law may be stated as,

For a given mass of gas, at constant pressure, its volume (V) varies directly as its absolute temperature (T).

V a T

or

V / T =       Constant

Based on charle's law, the pressure - temperature relation is deduced as, for a given quantity of a gas, at constant volume, the pressure (P) varies directly as its absolute temperature (T)

P a T

or

P / T  =       Constant

where T is temperature in kelvin.

The equation of state for an ideal gas

Gases which obey Boyle's law and Charle's law are known as ideal gases. By combining these two laws, an equation of state of an ideal gas can be derived.

According to Boyle's law at constant temperature,

P a 1 / V

From Charle's law

P a T (at constant volume)

By combining these proportionalities,

P a T/V

Or

PV a T

PV = RT

where `R' is a proportionality constant, commonly called as the gas constant. Generally, the ideal gas equation is written as

PV = n RT

where `n' is the number of moles of the gas.

No. of moles = Mass of the gas in gram / Molecular mass of the gas =  m / M = mol

PV =  ( m / M ) RT

m =  mass of the gas.

The ideal gas equation can be written for a constant mass of a gas as,

P1 V1 / T1  =  P2 V2 / T2

Standard temperature and Pressure (S.T.P)

The conditions of a gas system present at standard temperature and standard pressure are its temperature at 273K and its pressure being at normal atmospheric pressure namely 1.013 x 105 Nm-2 (1 atm). Value of R (Gas constant) depends on the different units of pressure and volume.

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