Assume that one mole of a monatomic (CV,m = 2.5R) ideal gas undergoes a reversible isobaric expansion at 1 bar and the volume increases from 0.5 L to 1 L. (a) Find the heat per mole, the work per mole done, and the change in the molar internal energy, ΔUm, the molar enthalpy, ΔHm, for this process. b) What are the entropy changes ΔSm of the system and of the surroundings? Is this process spontaneous? Justify your answer.
Heat change when one mole of monoatomic gas undergoes a a reversible isobaric expansion at 1 bar and the volume increases from 0.5 L to 1 L is given by
W = -P(V) = -P(V2-V1)
W = -1(1-0.5) = -0.5 L.atm (1 L.atm = 101.3 J)
W = -0.5*101.3 J = -50.65 J
For an ideal gas expansion at constant temperature i.e., dT = 0, U = 0
From first law of thermodynamics, U =Q+W = 0 (since U=0)
Q = -W = -(-50.65) J = 50.65 J = 0.050 KJ/mol
the molar enthalpy, ΔHm = U+PV
since U=0, ΔHm = PV = 0.050 KJ/mol
Change in entropy, S = ΔHm/T = 0.050/273 = 1.83*10^-4 J.K
since the change in entropy is +ve the process is spontaneous.
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