One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27°C to 37°C.
Question:
One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27°C to 37°C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true?
$\left[\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{k}^{-1}\right]$
Correct Option: , 4
Solution:
Since, each vibrational mode, corresponds to two degrees of freedom, hence, f = 3 (trans.) + 3(rot.) + 8 (vib.) = 14
$\& \quad \gamma=1+\frac{2}{f}$
$\gamma=1+\frac{2}{14}=\frac{8}{7}$
$\mathrm{W}=\frac{\mathrm{nR} \Delta \mathrm{T}}{\gamma-\mathrm{l}}=-582$
As $\mathrm{W}<0$. work is done on the gas.