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One mole of a gas enclosed in a vessel is heated at constant pressure through 1K. Work done by the gas is

One mole of a gas enclosed in a vessel is heated at constant pressure through 1K. Work done by the gas is

Grade:11

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
3 years ago
Answer ::

For 1 mol of an ideal gas, ∆E = Cv*∆T
Heat transfer, Q = Cp* ∆T, because heat is transferred at constant pressure.
( Cp and Cv are the molar heat capacities at constant pressure and constant volume respectively for an ideal gas.)
From the 1st law of thermodynamics,
∆E = Q+W => W = ∆E - Q
W = Cv*∆T - Cp*∆T = (Cv-Cp)*∆T
For 1 mol of an ideal gas, Cp - Cv = R
W = - R*∆T
Putting, R = 8.314 J K^-1 mol^-1, ∆T = + 1 K
W = - 8.314 J mol^-1
Note the -ve sign, the work is done by the ideal gas in its expansion at constant pressure when temperature rises by 1K (or 1C).

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