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Chapter 19: Problem 18

A system goes from state 1 to state 2 and back to state \(1 .\) (a) Is \(\Delta E\) the same in magnitude for both the forward and reverse processes? (b) Without further information, can you conclude that the amount of heat transferred to the system as it goes from state 1 to state 2 is the same or different as compared to that upon going from state 2 back to state $1 ?(\mathbf{c})$ Suppose the changes in state are reversible processes. Is the work done by the system upon going from state 1 to state 2 the same or different as compared to that upon going from state 2 back to state \(1 ?\)

Short Answer

Expert verified
The magnitudes of the change in internal energy for both forward and reverse processes are the same, but we cannot conclude whether the amount of heat transferred will be the same or different without more information. If the processes are reversible, the work done by the system going from state 1 to state 2 is equal in magnitude and opposite in sign to the work done going from state 2 back to state 1.

Step by step solution

01

(a) Comparison of Change in Internal Energy Magnitudes

In thermodynamics, the change in internal energy, denoted by \(\Delta E\), is given by the difference in internal energy between the final and initial states: \[\Delta E = E_\text{final} - E_\text{initial}\] For the forward process (state 1 to state 2), \[\Delta E_\text{forw} = E_2 - E_1\] For the reverse process (state 2 to state 1), \[\Delta E_\text{rev} = E_1 - E_2 = -(E_2- E_1)\] Since the magnitude of both forward and reverse processes only depends on the difference between the two states and not its direction, we can conclude that the magnitudes of the change in internal energy for both processes are the same.
02

(b) Comparison of Heat Transfers

Without further information regarding the processes taking place between state 1 to state 2 and state 2 to state 1, it is not possible to conclude whether the amount of heat transferred to the system in these two processes will be the same or different. The heat transfer depends on the path taken during the process, and different paths can result in different amount of heat transfer.
03

(c) Comparison of Work Done: Reversible Processes

If the changes in state are reversible processes, we can use the concept of reversibility in thermodynamics to compare the work done by the system. In a reversible process, the system is always in thermodynamic equilibrium and no energy is lost. Thus, the work done during one reversible process can be completely recovered during its reverse process. For reversible processes going from state 1 to state 2 and then back to state 1, the work done by the system upon going from state 1 to state 2 is equal in magnitude and opposite in sign to the work done upon going from state 2 back to state 1.

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Most popular questions from this chapter

Indicate whether each of the following statements is trueor false. If it is false, correct it. (a) The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends entirely on the value of $\Delta H\( for the process \)\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) .$ (b) The reaction of \(\mathrm{Na}(s)\) with \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d) Spontaneous processes in general require that work be done to force them to proceed. (e) Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.

The reaction $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)$ is highly spontaneous. A classmate calculates the entropy change for this reaction and obtains a large negative value for \(\Delta S^{\circ}\). Did your classmate make a mistake in the calculation? Explain.

The reaction $$ \mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons 3 \mathrm{~S}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ is the basis of a suggested method for removal of \(\mathrm{SO}_{2}\) from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (a) What is the equilibrium constant for the reaction at $298 \mathrm{~K} ?(\mathbf{b})$ In principle, is this reaction a feasible method of removing \(\mathrm{SO}_{2}\) ? (c) If \(P_{5 \mathrm{O}_{2}}=P_{\mathrm{H}_{2}}\) s and the vapor pressure of water is \(3.33 \mathrm{kPa}\), calculate the equilibrium \(\mathrm{SO}_{2}\) pressure in the system at \(298 \mathrm{~K}\). (d) Would you expect the process to be more or less effective at higher temperatures?

The potassium-ion concentration in blood plasma is about $5.0 \times 10^{-3} \mathrm{M}$, whereas the concentration in muscle-cell fluid is much greater \((0.15 \mathrm{M})\). The plasma and intracellular fluid are separated by the cell membrane, which we assume is permeable only to \(\mathrm{K}^{+}\). (a) What is \(\Delta G\) for the transfer of \(1 \mathrm{~mol}\) of \(\mathrm{K}^{+}\) from blood plasma to the cellular fluid at body temperature \(37^{\circ} \mathrm{C} ?\) (b) What is the minimum amount of work that must be used to transfer this \(\mathrm{K}^{+} ?\)

Predict the sign of the entropy change of the system for each of the following reactions: (a) $\mathrm{CO}(g)+\mathrm{H}_{2}(g) \longrightarrow C(s)+\mathrm{H}_{2} \mathrm{O}(g)$ (b) $2 \mathrm{O}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$ (c) $\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{HCl}(g)+\mathrm{NH}_{3}(g)$ (d) $2 \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}(g)$
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