Mechanics of Fluids and Pressure - Part VII

6. Boyleís law and Charlesí law  
We have seen how density, volume and pressure are interconnected in case of fluids. If the pressure is high, gases can be compressed, their volumes reduced and density increased.  Liquids are not as compressible as gases, hence the volume, density, pressure dependence on each other is not pronounced as in the case of gases.

In 1662, an Irish scientist, Robert Boyle made the following observations in case of gases.

1.      At a constant temperature, the volume of a gas is inversely proportional to the pressure.

                     1
V     
               P

2.      At a constant temperature, density of a gas is directly proportional to the pressure. 

D         P

Consider the following diagram:

Let V₁ be the volume of gas enclosed in the vessel, in first case A. Let the pressure exerted by the gas be P₁.

Now let some pressure be applied on the gas. Let the new pressure be P₂. We can see logically that on application of the pressure, the volume shrinks. Thus volume decrease as pressure increases. This is shown in case B.

This can be stated as Boyleís Law :  For a constant temperature, the volume of a given mass of gas varies inversely as the pressure on the gas.

                    1
      V     
                    P

      PV = K                                          K = constant

 Putting the law in a more general way, we get

 P_oV_o = P₁V₁ = P₂V₂  =ÖÖÖ= K

When temperature of a given mass of gas is increased, instead of pressure, we know that the gas will expand. The reverse is also true. Charlesí Law gives the manner in which the volume of a gas changes with temperature. The law states that for a constant pressure on a given mass of gas, the volume is directly proportional to the temperature.

V      T

   V
  =         constant         ( this constant of proportionality is not the same as that
   T                                         given in Boyleís law)

Putting the law in a more general way, we get

    V                 V₁                 V₂       
    =          =             = ÖÖ. constant
    T                  T₁                 T

The combination of Boyleís law and Charlesí law is given by gas equation. It states that for both pressure and temperature remaining constant, for a given mass of gas, we have

                                    1                                 T
V      T,         V       ,    thus    V  
                                    P                                 P

 P V
       = constant = R      R is known as gas constant.
   T
(more generally it is PV/T = nR)

 Boyleís and Charlesí law hold good only for ideal gases. Real gases do not obey the law at high temperatures and low pressures. Ideal or perfect gas is a gas that obeys Boyleís Law and Charlesí law strictly under all conditions of temperatures and pressures.

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