One mole of an ideal gas passes through a process where pressure and volume obey the relation P = P o 1 - 1 2 V o V 2 . Here P o and V o are constants. Calculate the change in the temperature of the gas if its volume changes from V o to 2 V o .

Step-by-step solution

For ideal gas, P V = n R T Therefore, n R T V = P 0 1 - 1 2 V 0 V 2 ⇒ T = P 0 V R 1 - 1 2 V 0 V 2 Therefore, the change in temperature is: Δ T = T f - T i = P 0 2 V 0 R 1 - 1 2 V 0 2 V 0 2 - P 0 V R 1 - V 0 2 2 V 0 2 = 5 P 0 V 0 4 R