Boyle’s and Charles Law - Gas Laws | Physics Grade XI

Gas Laws

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Boyle’s and Charles Law - Gas Laws | Physics Grade XI

Boyle’s Law and Charles Law - Gas Laws

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 P1, V1 are the initial pressure and the volume and P2, V2 are the final pressure and volume, then
       P1V1 = P2V2 = constant
On 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.
Boyle's law graph
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 V0 at θ degree Celsius. Then from above statement, we can write
     V = V0 (1 + γpθ)
Where γp is a constant called coefficient of expansion of the gas at constant pressure or volume coefficient of gas. Or V = V0 + V0γpθ
 
Experimentally the value of γp is found 1/273 K
So above equation reduces to V = V0 + V0 (1/273) θ
      or V = V0 (1 + 1/273 θ)
     or, V = V0 {(273+θ)/273}
 
     or, V = V0 (T/T0)
Where, 273 + θ = T, is taken as the absolute temperature at θ degree Celsius and 273 = T0 is the absolute temperature at 0 degrees Celsius.
     .: V0/T0 = 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 P0 at 0-degree Celsius and P at θ degree Celsius. Then from above statement, we can write
     P = P0 (1 + γVθ)
Where γv is a constant called coefficient of expansion of the gas at constant volume or pressure coefficient of gas. or P = P0 + P0γvθ
Experimentally it is found that the value of γv is 1/ 273
So the above equation reduces to P = P0 + P0 (1/273)θ
     or P = P0 (1 + (1/273)θ)
     or, P = P0 {(273+θ)/273}
     or, P = P0 (T/T0)
Where, 273 + θ = T, is taken as the absolute temperature at θ degree Celsius and 273 = T0 is the absolute temperature at 0 degree Celsius.
     .: P0/ T0 = 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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