**Gas Laws**

Boyle’s law states that on temperature keeping constant, the volume of the given mass of a gas is inversely proportional to the pressure. Mathematically, it can be written as

V α 1/P

or, PV = constant …... (i)

If P

_{1}, V_{1}are the initial pressure and the volume and P_{2}, V_{2}are the final pressure and volume, then P

_{1}V_{1}= P_{2}V_{2}= constantOn plotting a graph between P and V and P and 1/V on temperature keeping constant, we get the following curves as shown in the figure which proves Boyle's law.

It may be noted that the gases do not obey Boyles law strictly at all values of temperature and pressure. This law is obeyed at higher temperature and low pressure.

**Charles Law**

Charles law states that the volume of the given mass of a gas at constant temperature increases or decreases by a constant fraction of its volume at 0 degree Celsius from each degree rise or fall in temperature. Let us consider a gas of volume V

_{0}at θ degree Celsius. Then from above statement, we can write V = V

_{0}(1 + γ_{p}θ)Where γ

_{p}is a constant called coefficient of expansion of the gas at constant pressure or volume coefficient of gas. Or V = V_{0}+ V_{0}γ_{p}θExperimentally the value of γ

_{p}is found 1/273 KSo above equation reduces to V = V

_{0}+ V_{0}(1/273) θ or V = V

_{0}(1 + 1/273 θ) or, V = V

_{0}{(273+θ)/273} or, V = V

_{0}(T/T_{0})Where, 273 + θ = T, is taken as the absolute temperature at θ degree Celsius and 273 = T

_{0}is the absolute temperature at 0 degrees Celsius. .: V

_{0}/T_{0}= V/ T = constant or, V/T = constant

or, V α T

Thus, this law also states that in pressure keeping constant, the volume of a given mass of the gas is directly proportional to the absolute temperature.

**Charles Pressure law**

This law states that at constant volume, the pressure of the given mass of a gas increases or decreases by a constant fraction of its pressure at 0 degree Celsius for each degree rise or fall in temperature. Let us consider a gas at a pressure P

_{0}at 0-degree Celsius and P at θ degree Celsius. Then from above statement, we can write P = P

_{0}(1 + γ_{V}θ)Where γ

_{v}is a constant called coefficient of expansion of the gas at constant volume or pressure coefficient of gas. or P = P_{0}+ P_{0}γ_{v}θExperimentally it is found that the value of γ

_{v}is 1/ 273So the above equation reduces to P = P

_{0}+ P_{0}(1/273)θ or P = P

_{0}(1 + (1/273)θ) or, P = P

_{0}{(273+θ)/273} or, P = P

_{0}(T/T_{0})Where, 273 + θ = T, is taken as the absolute temperature at θ degree Celsius and 273 = T

_{0}is the absolute temperature at 0 degree Celsius. .: P

_{0}/ T_{0}= P/ T = constant or, P/ T = constant

or, P α T

Thus, this pressure law states that at constant volume, the pressure of the given mass of a gas is directly proportional to the absolute temperature.

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