A polyatomic gas with six degrees of freedom does 75 j of work. when it is expanded at constant pressure, the heat given to gas is
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Degree of freedom , f = 6
We know, the relation between degree of freedom and γ
e.g., γ = 1 + 2/f
γ = 1 + 2/6 = 4/3
we also know, ∆Q = ∆U + W [ from 1st law of thermodynamics ]
∆Q = hear at constant pressure e.g., ∆Q = nCp∆T
∆Q = nγ/(γ - 1) ∆T
∆U = heat at constant volume e.g., ∆U = nCv∆T
∆U = n/(γ - 1) ∆T
Now, ∆Q/W = ∆Q/(∆Q - ∆U) ={ nγ/(γ-1)∆T}/{nγ/(γ - 1)∆T - n/(γ - 1)∆T }
∆Q/W = γ/(γ - 1) = 4/3/(4/3-1) = 4
so, ∆Q = 4 × W
But W is given 75J
so, ∆Q = 4 × 75 = 300J
We know, the relation between degree of freedom and γ
e.g., γ = 1 + 2/f
γ = 1 + 2/6 = 4/3
we also know, ∆Q = ∆U + W [ from 1st law of thermodynamics ]
∆Q = hear at constant pressure e.g., ∆Q = nCp∆T
∆Q = nγ/(γ - 1) ∆T
∆U = heat at constant volume e.g., ∆U = nCv∆T
∆U = n/(γ - 1) ∆T
Now, ∆Q/W = ∆Q/(∆Q - ∆U) ={ nγ/(γ-1)∆T}/{nγ/(γ - 1)∆T - n/(γ - 1)∆T }
∆Q/W = γ/(γ - 1) = 4/3/(4/3-1) = 4
so, ∆Q = 4 × W
But W is given 75J
so, ∆Q = 4 × 75 = 300J
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