Boyle's law states that the volume of a gas is inversely proportional to its pressure when temperature is kept constant. Charles's law states that the volume of a gas is directly proportional to its temperature when pressure is kept constant. An ideal gas obeys both Boyle's law and Charles's law, such that its volume is directly proportional to temperature and inversely proportional to pressure, as expressed by the equation PV=nRT.

2. According to Boyle’s law,
The volume of a given mass of a gas
is inversely proportional to the pressure
at a constant temperature.

3. Given V α 1/P at constant T
Or V=1/P * Constant
Or PV=constant
Or PV= k(constant)

4. Let V1 be the initial volume and V2 be the final
volume
And P1 be the initial pressure and P2 be the final
Pressure
So the equation is given by

5. According to the Charle’s Law
Volume of a given mass of a gas is directly
proportional to the Temperature at
constant pressure.

6. By Charle’s Law, V α T
Or V=T*constant
Or V/T=constant
Or V/T=m(constant)

7. Let V1 be the initial volume and V2 be the final
volume
Let T1 be the initial temperature and T2 be the
final temperature
So the equation is given by

8. An ideal gas is one which obeys both Boyle’s Law
and Charle’s Law.
By Boyle’s Law
V α 1/P-------------------------------------(1) at const. T
V α T----------------------------------------(2) at const. P
Combining the 2 equations
V α T/P
Or V=T/P * constant

9. i.e PV=RT which is an expression for an ideal gas
for 1 mole of any gas
So PV=nRT for n moles of any gas
Where
P=Pressure
V=Volume
n= n number of moles of gas
R=Universal gas constant whose value for mole of
gas=8.314 J mol-1 K-1