Question

derive boyles law on basis of the kinetic theory of gases

Answer 1

Boyle's Law from Kinetic theory of gases

From kinetic theory of gases, we have

P=13MVc^¯2

or,PV=13Mc^¯2

Since C^¯2∝T, if the temperature of the gas is kept constant, for given mass of a gas (i.e. M = constant),

PV=constant

i.e.p∝1V

It means pressure of the given mass of a gas is inversely proportional to it's volume at constant temperatures which is Boyle's law.

Charle's Law from Kinetic theory of gases

From kinetic theory of gases, we have

P=13MVc^¯2

or,V=13MPc^¯2

Since C^¯2∝T, if the pressure of the gas is kept constant, for given mass of a gas, we have

v∝T

It means volume of the given mass of a gas is directly proportional to it's absolute temperature at a constant pressure which is Charle's law.

Law of pressure from Kinetic theory of gases

here,

P=13MVc¯^2

Since C¯^2∝T and at constant volume of a gas, the above equation becomes

P∝T

It means pressure of the gas is directly proportional to its absolute temperature at constant volume which is law of increase of pressure.

Perfect Gas Equation from Kinetic theory of gases

From kinetic theory of gases, we have

P=13MVc¯^2

or,V=13MPc¯ ^2…(i)

Since C¯2∝T so, equation (i) becomes,

PV∝T

or,PV=RT

Where R is the constant foe one mole of an ideal gas. This equation is the perfect gas equation.

Answer 2

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Mathematically, Boyle's law can be stated as

{\displaystyle P\propto {\frac {1}{V}}}Pressure is inversely proportional to the volume.

or

{\displaystyle PV=k}Pressure multiplied by volume equals some constant {\displaystyle k}.

where P is the pressure of the gas, V is the volume of the gas, and k is a constant.

The equation states that the product of pressure and volume is a constant for a given mass of confined gas and this holds as long as the temperature is constant. For comparing the same substance under two different sets of conditions, the law can be usefully expressed as

{\displaystyle P_{1}V_{1}=P_{2}V_{2}.}

The equation shows that, as volume increases, the pressure of the gas decreases in proportion. Similarly, as volume decreases, the pressure of the gas increases. The law was named after chemist and physicistRobert Boyle, who published the original law in 1662

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