Gases

Question:  How will you verify the law experimentally? Give graphical explanation of the law?

Answer:    

Explanation.

            The law can be verified by a simple experiment as shown in figure below.

Figure:   Verification of Boyle's Law

It consists of a cylinder fitted with a piston and a manometer. One dm³ of a gas at 2 atm and 25 ^οC is enclosed in the cylinder. When the pressure is doubled (4 atm), the is reduced to ½ dm^3.  When the pressure is increased 3 times (6 atm), volume of the gas  the volume of the gas is reduced to 1/3 dm³.

Hence ,               P_IV_I   = 2 atm x 1 dm³     = 2 atm. dm³

                            P₂V₂  = 4 atm x 1/2dm³   ₌  2 atm. dm³

                            P₃V₃  = 6 atm x 1/3dm³  = 2 atm. dm3

                            P₁V₁= P₂V₂ = P₃V₃ = constant at constant 

Graphical Explanation of Boyle's Law:

In the above experiment, at constant temperature when pressure is varied and volume is noted against each pressure. Graphical explanation of the law is then given in a variety of ways. A plot of V Versus P gives a hyperbolic curve.

              Figure:  Isotherm of gas at 0 ^οC

Such curves drawn at constant temperature are called isotherms. At higher temperature the gas expands and the curve goes away from to two axes.

Figure. Isotherms of a gas at different temperature

A plot P verses 1/V is a straight line. The straight line meets at origin where the pressure is close to zero and the volume is so high that, l/v becomes almost equal to zero. At higher constant temperature, the straight line will be closer to x-axis.

Figure: A plot between P and 1/V

A plot of PV versus P at constant temperature is a straight line parallel to X-axis for ideal gas . Any deviation from straight line will make the gas non-ideal.

                       Figure: A Plot between pressure and product PV

Question . State and explain Charle’s Law

Answer: 

Statement: ‘‘Volume of a given mass of a gas is directly proportional to 

absolute temperature at constant pressure”. Or

Mathematically

 

Explanation: A known quantity of a gas is taken in a cylinder fitted with a piston. Let the volume of the gas be V₁ at temperature T₁ When gas is heated, its volume changes to V₂ and temperature to T₂. It is seen that.

Figure. Verification of Charle’s law

Figure:Diagramatic representation of Charl's Law

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