Grade 12th passPhysical Chemistry
Calculate the entropy change when 14gm nitrogen gas expands reversible from 2l to 20l at 27°c
Calculate the entropy change when 14gm nitrogen gas expands reversible from 2l to 20l at 27°c
1 Answer
Vikas TU
Dear student
For a closed system undergoing a reversible change,
dU = T.dS - P.dV ..................(1)
P,T - Pressure and temperature of the system
dS = differential change in entropy of the system
dV= differential change in volume of system
U = internal energy of the system
Internal energy of an ideal gas is a function of temperature only. The given condition being an isothermal expansion, there won’t be change in the internal energy of the system i.e. gas.
Thus equation (1) would be transformed as,
T. dS = P. dV ..............2
dS = (P/T). dV .............. 3
On integrating on both sides with initial final conditions,
del(S) = nR. ln(V2/V1)
V2 =final volume of the gas
V1 = Initial volume of the gas
n = number of moles of the gas
From the problem, V2 = 20L, V1 = 2L, n = 2 mol, R (universal gas constant) = 8.314 J/(mole.K)
Thus substituing the values, change in entropy of the system is
del(S) = 38.287 J/K
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