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?
$\left[R=8.314Jmo{l}^{-1}{k}^{-1}\right]$

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

Answer 1

Answer: (B)

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