One mole of a monatomic ideal gas at an initial temperature T is adiabatically compressed such that the work done on the gas is 3 2 RT . The ratio of the final volume to the initial volume of the gas is:

Step-by-step solution

For a monatomic ideal gas, the molar heat capacity at constant volume is C_v = 3 2 R and the ratio of specific heats is = 5 3 . According to the first law of thermodynamics for an adiabatic process, the work done on the gas equals the increase in its internal energy: W_ on = U = n C_v (T₂ - T₁) Substituting the given values: 3 2 RT = (1) ( 3 2 R ) (T₂ - T) T₂ - T = T T₂ = 2T For an adiabatic process, the temperature and volume are related by: T₁ V₁^ - 1 = T₂ V₂^ - 1 Substituting - 1 = 5 3 - 1 = 2 3 : T V₁^ 2/3 = (2