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11.Thermodynamics
medium
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?
A
Work done on the gas is close to $582\, J$
B
Work done by the gas is close to $332\, J$
C
Work done by the gas is close to $582 \,{J}$
D
Work done on the gas is close to $332 \,J$
(JEE MAIN-2021)
Solution
For an ideal gas, 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.
Standard 11
Physics
