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  • 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? <img alt="\left [ R=

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 [ R=8.314\: J\: mol^{-1}k^{-1} \right ]
Option: 1 Work done by the gas is close to 332 J
Option: 2 Work done on the gas is close to 582 J
Option: 3 Work done by the gas is close to 582 J
Option: 4 Work done by the gas is close to 332 J

Answers (1)

best_answer

\begin{aligned} n=1 \mathrm{mol} \\ \end{aligned}

\begin{aligned} \Delta T &=10 \end{aligned}
Total degree of freedom = 3 Translational +3 Rotational +8 vibrational mode
\because For each vibrational mode there are 2 degree of freedom

\begin{aligned} &f=14 \\ &\gamma =\frac{2+f}{f}=\frac{16}{14}=\frac{8}{7} \end{aligned}

\begin{aligned} W &=\frac{-n R \Delta T}{\gamma-1}=\frac{-1 \times 8.314 \times 10}{\frac{8}{7}-1} \\ &=-8.314 \times 70 \\ W &=-582 \mathrm{~J} \end{aligned}
Negative work \rightarrowWork done on the gas.

The correct option is (2)
 

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vishal kumar

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