An isothermal reversible expansion, for which pV=constant as shown by the curve

ID: 793661 • Letter: A

Question

joining State A and State B, takes a system from State A to State B along the curved

line on the diagram above. The pressure of State A is 50 x 10^5 Pa and the pressure of

State B is 12.5 x 10^5 Pa. The system is also taken from State A to State B in two

irreversible steps as indicated by the pathways I and II in the diagram. Each irreversible

step involves expansion against a constant external pressure.

(a) How much heat is required for the isothermal reversible expansion from State A to State B?

(b) [What is ?H for the isothermal reversible expansion?

II) from State A to State B?

(d) If the system is an ideal gas determine the entropy change for the reversible

expansion from State A to State B, and calculate the increase in the number of

microstates for the system during expansion.

(e) Using a microscopic definition of work, heat and temperature, explain how the

populations and energy levels of the ideal gas molecules change during the

reversible expansion.

a) W = nRT*ln(Vb/Va) = Pa*Va*ln(Vb/Va) = 50*10^5*1*10^-3*ln(4) = 6931.4J

Q= U +w

Q = 0 + w, since change ni temperature is 0

Q = W = heat required = 6931.4 J

b) H = U + PV

dH = dU + nRdT = 0+0 = 0

Hence delta H = 0

c) wi = 20*10^5*1*10^-3 + 12.5*10^5*1*10^-3 = 3250 J

we = Pe*3*10^-3 J

Q = U + W

d) S = Q/T = 6931.4/T

T = PV/nR = Pa*Va/n*8.314

S = kB* ln(W)

kB = 1.43*10^-23 J/K

W = increase in microstates

S = entropy calculated above

e) Heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in energy levels of the system

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