A certain amount of a non-linear polyatomic gas having f active vibrational modes undergoes an isobaric expansion. If Q is the heat supplied to the gas and W is the work done by the gas, the ratio W Q is:

Step-by-step solution

For a non-linear polyatomic gas, the number of translational degrees of freedom is 3 and rotational degrees of freedom is 3. Each active vibrational mode contributes R to the molar heat capacity at constant volume ( C_v ). Thus, C_v = 3 2 R + 3 2 R + fR = (3+f)R The molar heat capacity at constant pressure is: C_p = C_v + R = (4+f)R In an isobaric process, the work done by the gas is W = nR T and the heat supplied is Q = nC_p T . Therefore, the ratio is: W Q = nR T nC_p T = R C_p = R (4+f)R = 1 4+f Answer: 1 4+f