Question

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27^{\circ} C$ to $37^{\circ} C$. If the ideal gas is composed of polyatomic molecule that has $4$ vibrational modes, which of the following is true?
$\left[R=8.314 \,J\, mol ^{-1} k^{-1}\right]$

• A. work done by the gas is close to $332 \,J$
• B. work done on the gas is close to $582 \,J$
• C. work done by the gas is close to $582\, J$
• D. work done on the gas is close to $332 \,J$

Answer 1

Answer: (B)

Since, each vibrational mode, corresponds to two degrees of freedom,
hence, $f=3$ (trans.) $+3$ (rot.) $+8$ (vib.) $=14$
$\& \,\gamma=1+\frac{2}{f} $
$\gamma=1+\frac{2}{14}=\frac{8}{7} $
$W=\frac{n R \Delta T}{\gamma-1}=-582$
As $W< 0$.
Work is done on the gas.