Equal numbers of moles of two different ideal gases, one monoatomic and the other rigid diatomic, are subjected to adiabatic expansion. Both gases experience the exact same decrease in temperature during their respective expansions. The ratio of the work done by the monoatomic gas to the work done by the diatomic gas is:

Step-by-step solution

For an adiabatic process, the heat exchanged is zero, so the work done by the gas equals the decrease in its internal energy: W = - U . The change in internal energy for n moles of an ideal gas is given by U = nC_v T . For the monoatomic gas, the molar heat capacity at constant volume is C_ v1 = 3 2 R . For the rigid diatomic gas, the molar heat capacity at constant volume is C_ v2 = 5 2 R . Since both gases have the same number of moles n and undergo the same temperature drop T , the ratio of the work done is: W₁