A gas at `27^@ C` in a cylinder has a volume of 4 litre and pressure `100 Nm^-2`.
(i) Gas is first compressed at constant temperature so that the pressure is `150 Nm^-2` . Calculate the change in volume.
(ii) It is then heated at constant volume so that temperature becomes `127^@ C`. Calculate the new pressure.

Explanation

(i) here,
`T_(1)=27^(@)C = (27+273)K = 300K, V_(1)= 4 litre`
`P_(1)= 100Nm^(-2), P_(2)= 150 N//m^(2), V_(2) =?`
From Boyle's law , `P_(2) V_(2)= P_(1)V_(1)`
`:. V_(2) =(P_(1)V_(1))/(P_2) = (100 xx 4)/(150) = 2.67 litre`
Change in volume = `V_(1)-V_(2) = 4 - 2.67`
`=1.33 litre`
(ii) Now, `T_(2)=127^(@)C=(127+273)K=400K`,
`P_(2)=?`
From Gay Lausac's law, `(P_2)/(P_1) = (T_2)/(T_1)` ,
`P_(2)= (T_2)/(T_1) P_(1) = (400)/(300) xx 150 = 200 Nm^(-2)`.