During an experiment, an ideal gas is found to obey an additional law VP ^2= constant. The gas is initially at temperature ' T ' and volume ' V '. What will be the temperature of the gas when it expands to a volume 2 V ?

Step-by-step solution

aligned & PV nRT & P = RT ~V ...(i) & VP ^2= constant ... (given) & V ( RT ~V )^2= constant ... (from(i)) & R ^2 ~T ^2 ~V = constant T ^2 ~V = constant ( given T₁=T ) & ( T ₁ ~T ₂ )^2= V ₁ ~V ₂ & ~T ₁ ~T ₂ = V 2 ~V & ~T ₂= 2 ~T aligned