A certain amount of an ideal gas is enclosed in a cylinder fitted with a movable piston. What would be the changes of the volume of the gas in the following processes?
(i) The pressure of the gas is reduced by 25% at constant temperature.
(ii) The temperature of the gas is increased by 50% constant pressure.

Explanation

(i) According to Boyle's law, `P_(1)V_(1)=P_(2)V_(2)` when mass and temperature of a gas are constant. After the reduction of initial pressure `(P_(1))` by 25%, the final pressure `(P_(2))` becomes `(P_(1)-P_(1)xx(25)/(100))=0.75P_(1)`.
i.e., `P_(2)=0.75P_(1)`.
`therefore V_(2)=(P_(1)V_(1))/(P_(2))=(P_(1)xxV_(1))/(0.75P_(1))=(4)/(3)V_(1)`
Therefore, the change in volume `=(4)/(3)V_(1)-V_(1)=(V_(1))/(3)`
(ii) According to Charles' law, `V_(1)T_(2)=V_(2)T_(1)` when mass and pressure of a gas remains constant.
after increasing the initial temperature `(T_(1))` by 50%
the final temperature `(T_(2))` becomes
`(T_(1)+T_(1)xx(50)/(100))=1.5T_(1), i.e., T_(2)=1.5T_(1)`
`therefore V_(1)xx1.5T_(2)=V_(2)T_(2) or , V_(2)=1.5xxV_(1)`
`therefore`The change in volume`=1.5V_(1)-V_(1)=0.5V_(1)`.