3. Ideal gases! Calculate the change in entropy for one mole of ideal gas which

Question

3. Ideal gases! Calculate the change in entropy for one mole of ideal gas which expands from an initial volume of 2 L and initial temperature of 500 K to a final volume of 6 L under the following conditions. Pinitial refers to the pressure when Tinitial=500 K, Vinitial=2 L.

a. Irreversible expansion against a constant (and final) pressure of Pinitial/2.

b. Irreversible expansion against a vacuum…a ‘free expansion’.

c. Adiabatic irreversible expansion against a constant pressure of Pfinal.

d. Adiabatic reversible expansion.

Explanation / Answer

3)

a) Irreversible expansion against a constant (and final) pressure of Pinitial/2.

S (system) = nR ln V2/V1

S = 1 X 8.314 X ln (6/2) = 9.135 Joules / mol K

b) Irreversible expansion against a vacuum…a ‘free expansion

the work done = 0

Change in internal energy = 0
Change in entropy of system = S (system) = nR ln V2/V1

R = gas constant

S = 1 X 8.314 X ln (6/2) = 9.135 Joules / mol K

Entropy change of surrounding = 0

c) Adiabatic irreversible expansion against a constant pressure of Pfinal

S (system) = nR ln V2/V1

S = 1 X 8.314 X ln (6/2) = 9.135 Joules / mol K

d) Adiabatic reversible expansion

As delta Q = 0

So delta S = 0

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