(c) During a certain reversible process, the surroundings undergo an entropy change, ΔSsurr = -78 J/K. What is the entropy change of the system for this process?

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Identify the given entropy change of the surroundings, which is ΔSsurr = -78 J/K.

Understand that for a reversible process, the total entropy change of the universe (system plus surroundings) is zero. This is expressed as ΔSuniv = ΔSsys + ΔSsurr = 0.

Rearrange the equation to solve for the entropy change of the system (ΔSsys). This can be done by isolating ΔSsys on one side of the equation: ΔSsys = -ΔSsurr.

Substitute the given value of ΔSsurr into the equation: ΔSsys = -(-78 J/K).

Simplify the expression to find ΔSsys, which will be the positive value of the given ΔSsurr, indicating the entropy change of the system.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the amount of energy in a physical system that is not available to do work. Higher entropy indicates greater disorder, while lower entropy suggests more order. Understanding entropy is crucial for analyzing energy transformations and the direction of spontaneous processes.

Reversible Processes

A reversible process is an idealized process that occurs in such a way that the system and surroundings can be returned to their original states without any net change. In thermodynamics, reversible processes are characterized by equilibrium conditions and maximum efficiency. They serve as a benchmark for real processes, which are often irreversible and involve energy losses.

Second Law of Thermodynamics

The Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time. It implies that natural processes tend to move towards a state of maximum disorder or entropy. This law is fundamental in determining the direction of spontaneous processes and helps relate the entropy changes of the system and surroundings in reversible processes.

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Textbook Question

Indicate whether each statement is true or false. (c) In a certain spontaneous process the system undergoes an entropy change of 4.2 J/K; therefore, the entropy change of the surroundings must be -4.2 J/K.

Textbook Question

(a) Does the entropy of the surroundings increase for spontaneous processes?

Textbook Question

(b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of ΔS_surr?

Textbook Question

(a) What sign for Δ𝑆 do you expect when the pressure on 0.600 mol of an ideal gas at 350 K is increased isothermally from an initial pressure of 0.750 atm?

(b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process.

(c) Which of the following statements about this process are true? (i) The entropy change you calculated will be the same for at any other constant temperature. (ii) The value of Δ𝑆 you calculated is valid only if the compression is done irreversibly. (iii) If the number of moles of gas being compressed were decreased by a factor of three, the entropy change would increase by a factor of three.

Textbook Question

For the isothermal expansion of a gas into a vacuum, ΔE = 0, q = 0, and w = 0. (b) Explain why no work is done by the system during this process.

Textbook Question

(a) What is the difference between a state and a microstate of a system?