Question

During an experiment, an ideal gas is found to obey an additional law `pV^(2)`=constant. The gas is initially at a temperature T and volume V. Find the temperature when it expands to a volume 2V.

Answer 1

` PV_2 = constant `
` rArr ((P_1)(V_(1)^2)) = ((P_2)(V_(2)^2))`
` = (mRT_1)/(V_1) xx (V_(1)^2) = (mRT_2)/(V_2) xx (V_(2)^2)`
` rArr (mRT_1/V_1) xx (V_(1)^2) = (mRT_2/ V_2) xx (V_(2)^2).`
` rArr (T_1)(V_1) = (T_2)(V_2)`
` rArr TV= (T_2) xx (2V) `
` (T_2) = (T/2)`