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hw3 - Solution to Homework 3 3.1(a True Please see the...

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Solution to Homework 3 3.1 (a) True Please see the Equation (3.15) on Page 84 in the Levine's book. (b) True Please see the Equation (3.15) on Page 84 in the Levine's book. (c) True A Carnot cycle is defined as a reversible cycle. (d) False Work is not a state function. It depends on the process (path). 3.7 (a) False The entropy is a state function. So the change of state from 1 to 2 will produce the same change in entropy when carried out both irreversibly and reversibly. (b) True Heat q is not a state function. It depends on the path. (c) True According to the definition of change in entopy rev q dS T . (d) True The entropy is extensive. (e) True The molar entropy is intensive. (f) False According to the definition of change in entopy rev q dS T , the heat for an isothermal process is not necessarily zero. So the Δ S may not be zero. (g) False This is true only when the C v is regarded as a constant. However, in the real cases, C v varies as temperature changes. (h) False The process should be reversible. (i) False The entropy is a state function. If two states are connected by an irreversible process, we can construct a reversible process to link the initial and final states to calculate the change in entropy. (j) True According to the definition of change in entopy rev q dS T (k) True
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Those formulas only deal with the change in entropy instead of the value of S. 3.20 (a) False If the closed system releases some heat to the surroundings reversibly, Δ S can be negative. (b) False If the closed system releases some heat to the surroundings reversibly, Δ S can be negative. (c) True See Page 93 in the Levine s book. (d) True If it s a reversible process, Δ S=0; If it s an irreversible process, the entropy of a closed system must increase in an irreversible adiabatic process (For proof, please see Page 93-95 in the book). So Δ S cannot be negative. (e) True An isolated system is necessarily closed. Hence the reason is the same as (d). (f) False If the process is irreversible, Δ S may not be zero. (g) True The reason is the same as (d). (h) False This is true for isolated system instead of closed system. For more details, see Page 95-96 in the book. 3.21 Using rev q dS T , we have for the signs of Δ S: (a) dq rev >0 so Δ S>0. (b) dq rev >0 so Δ S>0.
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