JEE MAIN - Physics (2021 - 27th July Evening Shift - No. 4)
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? [R = 8.314 J mol$$-$$1 k$$-$$1]
work done by the gas is close to 332 J
work done on the gas is close to 582 J
work done by the gas is close to 582 J
work done on the gas is close to 332 J
Explanation
Since, each vibrational mode, corresponds to two degrees of freedom, hence, f = 3 (trans.) + 3 (rot.) + 4 $$ \times $$ 2 (vib.) = 14
& $$\gamma = 1 + {2 \over f}$$
$$\gamma = 1 + {2 \over {14}} = {8 \over 7}$$
$$W = {{nR\Delta T} \over {\gamma - 1}} = - 582$$
As W < 0. work is done on the gas.
& $$\gamma = 1 + {2 \over f}$$
$$\gamma = 1 + {2 \over {14}} = {8 \over 7}$$
$$W = {{nR\Delta T} \over {\gamma - 1}} = - 582$$
As W < 0. work is done on the gas.
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