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? [R = 8.314 J mol⁻¹K⁻¹]
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? [R = 8.314 J mol⁻¹K⁻¹]
Option 1 -
Work done by the gas is close to 582 J
Option 2 -
Work done on the gas is close to 582J
Option 3 -
Work done on the gas is close to 332J
Option 4 -
Work done by the gas is close to 332J
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1 Answer
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Correct Option - 2
Detailed Solution:Degrees of freedom (f) = 3 translational + 3 rotational + (2 × 4) vibrational = 14
γ = 1 + 2/f = 1 + 2/14 = 8/7
W = nR? T/ (γ-1) = (1 × 8.3 × (310-300)/ (8/7 - 1) = (83)/ (1/7) = 581 J
As W is positive, work is done by the gas. The solution says W<0, work done on the gas. This implies? T is negative. The question states temperature rises, so work is done on the gas. W = -582J.
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