A certain mass of gas in a cylinder at `27^(@)C` has a volume of 10 litre and pressure 100 `N//m^(2)`. (i) The gas is first compressed at constant temperature and the pressure is raised to 150 `N//m^(2)` . Find the change in volume. (ii) If the gas is then heated at constant volume and if the temperature is raised to `127^(@)C`, find the new pressure.

Explanation

`T_(1) = 2 7 + 273 = 300K, V_(1) = 10l , P_(1) = 100 N//m^(2)`
(i) The gas is compressed at constant temperature
`P_(2)= 150 N//m^(2) , V_(2) =?`
`P_(1) V_(1) = P_(2) V_(2)`
`V_(2) = (P_(1) V_(1))/( P_(2)) = ( 100 xx 10)/( 150) = 6.67 l`
Change in volume `= V_(1) - V_(2) = 10 - 6.67 = 3.33l`
(ii) The gas is heated at constant volume
`T_(2) = 127 + 273 = 400K, P_(2) = ?`
`( P_(1))/( T_(1)) = ( P_(2))/( T_(2)) , P_(2) = ( P_(1) T_(2))/( T_(1)) = ( 100 xx 400)/( 300) = 133.33N//m^(2)`