An ideal gas undergoes a process maintaining relation between pressure (P) and volume (V) as P = P_o (1 + ( V_o V )^2 )⁻¹ , where P_o and V_o are constants. If two samples A and B (two moles each) with initial volumes V_o and 3V_o respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, T_B - T_A is _____. ( R = gas constant)

Step-by-step solution

The given relation between pressure and volume is: P = P_o (1 + ( V_o V )^2 )⁻¹ For sample A, the initial volume is V_A = V_o . Substituting this into the given relation, the initial pressure P_A is: P_A = P_o (1 + ( V_o V_o )^2 )⁻¹ = P_o 2 Using the ideal gas equation PV = nRT for n = 2 moles, the initial temperature T_A is: T_A = P_A V_A nR = ( P_o 2 ) V_o 2R = P_o V_o 4R For sample B, the initial volume is V_B = 3V_o . Substituting this into the relation, the initial pressure P_B is: P_B = P_o (1 + ( V_o 3V_o )^