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Describe what the second law of thermodynamics states about the total entropy of an isolated system?
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The second law states that the total entropy of an isolated system can never decrease. It remains constant only when all processes within the system are reversible. Because real processes are irreversible, the total entropy of an isolated system always increases over time.
Explain why a hot object placed in a cooler room always transfers thermal energy to the room, rather than the reverse, even though both directions would conserve energy?
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Both directions conserve energy, satisfying the first law. However, the second law requires that the total entropy of the isolated system cannot decrease. Thermal energy flowing from hot to cold increases total entropy because energy spreads from a concentrated region to a more dispersed one. The reverse process would decrease total entropy, violating the second law.
Describe what it means for entropy to be a state function and explain the consequence of this property.
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A state function depends only on the current configuration of the system, not on the process used to reach that configuration. This means that the entropy of a system is fully determined by its present temperature, pressure, volume, and phase. Two systems in identical states have identical entropies regardless of their different histories.
A sealed, insulated container holds a hot block of metal on one side and a cold block on the other. Predict what happens to the total entropy of the system over time? Justify your reasoning.
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Thermal energy transfers spontaneously from the hot block to the cold block. Energy that was localized in the hot block spreads across both blocks. As energy disperses, the total entropy of the isolated system increases. The process continues until both blocks reach the same temperature — thermodynamic equilibrium — where entropy is at its maximum.
Indicate whether the following statement is correct: “At thermodynamic equilibrium, entropy is zero.” Justify your response.
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The statement is incorrect. At thermodynamic equilibrium, entropy is at its maximum value for that isolated system, not zero. Equilibrium is the state where energy is spread as uniformly as possible, so no further spontaneous processes can increase the entropy.
Describe how the entropy of a closed system can decrease without violating the second law of thermodynamics?
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A closed system can transfer energy to its surroundings. When energy leaves the system, the system’s entropy decreases. However, the surroundings gain that energy, so their entropy increases by an equal or greater amount. The total entropy of the isolated combination of system plus surroundings never decreases, satisfying the second law.
An isolated container of gas spontaneously evolves toward thermodynamic equilibrium. Indicate whether the entropy of the gas increases, decreases, or remains constant during this process? Justify your response.
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The entropy of the gas increases. An isolated system exchanges no energy or matter with its surroundings, so the second law requires that its total entropy never decreases. Because the process is spontaneous and irreversible, the entropy increases until the system reaches equilibrium, where it reaches its maximum value.
A student claims: “Placing water in a freezer decreases the water’s entropy, so the second law is violated.” Indicate whether this claim is correct? Justify your response.
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The claim is incorrect. The water is a closed system, not an isolated one, because it exchanges energy with the freezer. As the water loses thermal energy, its entropy decreases. However, the freezer’s motor and the surrounding environment gain entropy by a greater amount. The total entropy of the isolated combination still increases, consistent with the second law.