In a certain thermodynamical process, the pressure of a gas depends on its volume as k V 3 . The work done when the temperature changes from 100   ° C to 300   ° C will be x n R where n denotes number of moles of a gas find x ;

Step-by-step solution

P = k V 3 T i = 100   ° C   &   T f = 300   ° C Δ T = 300 - 100 Δ T = 200   ° C P = k V 3 now P V = n R T ∴   k V 4 = n R T now 4 k V 3 d V = n R d T ∴     P d V = n R d T / 4 ∴ Work = ∫ P d V = ∫ n R d T 4 = n R 4 Δ T = 200 4 × n R = 50 n R