Question

One mole of an ideal gas is taken through an adiabiatic 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?
$[R=8.314{\text{Jmol}}^{-1}{\text{k}}^{-1}$]

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

Answer 1

The correct option is B work done on the gas is close to $582\text{J}$

Since, each vibrational mode, corresponds to two degrees of freedom, hence,
$f=3\left(\text{trans.}\right)+3\left(\text{rot}\right)+8\left(\text{vib}\right)=14$
Also, we know that
$\gamma =1+\frac{2}{f}$
$\Rightarrow \gamma =1+\frac{2}{14}=\frac{8}{7}$
Now, work done in adiabatic process is given by
$W=\frac{nR(T_1-T_2)}{\gamma -1}=\frac{1\times 8.314\times (-10)}{(\frac{8}{7}-1)}=-582\text{J}$
as $W<0$, work is done on the gas.