1. If the temperature of a gas is increased by 4x, its volume A. will increase by 4x.
2. If the pressure of a gas is decreased by 4x, its volume A. will increase by 4x.
The combined gas law combines the three gas laws; Boyle's law, Charles law and Gay Lussac's law together relating pressure, temperature & volume and states thus:
"The ratio of product of Pressure and Volume to that of its Temperature is a constant."
In mathematical terms,
[tex]\frac{PV}{T} =constant\\\\\frac{P_1V_1}{T_1} = k\\\\\frac{P_2V_2}{T_2} = k\\\\\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}[/tex]
where P1, V1, T1 are the initial values and P2, V2, T2 the final values.
Therefore,
[tex]V\ \alpha\ T[/tex] .......................................(1)
[tex]P\ \alpha\ \frac{1}{V}[/tex] ......................................(2)
1. If temperature of gas is increased by 4x, keeping pressure constant, from(1) since the volume of gas is directly proportional to its temperature (by Charles' law); it will increase in the same rate as the temperature is increased. Hence, the volume will increase by 4x.
2. If the pressure of a gas is decreased by 4x, keeping temperature constant, from (2), since the pressure of a gas is inversely in proportion to its volume (by Boyles' law), a decrease in pressure leads to increase in volume and vice versa. Hence, the volume will increase by 4x.
