One mole of an ideal polyatomic gas ( = 4 3 ) at an initial temperature T expands adiabatically. If the work done by the gas during this process is 1.5 RT , the ratio of its final volume to the initial volume is:

Step-by-step solution

Given n = 1 mole, = 4 3 , and work done by the gas W = 1.5 RT . The work done in an adiabatic process is given by: W = nR(T_i - T_f) - 1 Substituting the given values: 1.5 RT = 1 R(T - T_f) 4 3 - 1 3 2 RT = R(T - T_f) 1 3 = 3R(T - T_f) Dividing both sides by 3R : T 2 = T - T_f T_f = T 2 For an adiabatic process, the temperature-volume relationship is: T_i V_i^ - 1 = T_f V_f^ - 1 T V_i^ 1 3 = ( T 2 ) V_f^ 1 3 2 = ( V_f V_i )^ 1 3 Cubing both sides, we get the ratio of the final volume to the initial volume: V_f V_i