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Which of the following relationships is correct for an isothermal reversible process involving an ideal gas?
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8. Thermochemistry
First Law of Thermodynamics
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According to the First Law of Thermodynamics, what are the expected signs of q_{sys} and q_{surr} when a system absorbs heat from its surroundings?
A
q_{sys} is positive, q_{surr} is negative
B
Both q_{sys} and q_{surr} are negative
C
q_{sys} is negative, q_{surr} is positive
D
Both q_{sys} and q_{surr} are positive
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Recall the First Law of Thermodynamics, which states that energy cannot be created or destroyed, only transferred. When heat is transferred, it moves from one part of the universe to another, such as from the surroundings to the system or vice versa.
Understand the sign convention for heat (\(q\)): if the system absorbs heat, \(q_{sys}\) is positive because energy is entering the system; if the system releases heat, \(q_{sys}\) is negative because energy is leaving the system.
Since the system absorbs heat from the surroundings, the surroundings must lose that heat. Therefore, the heat change for the surroundings, \(q_{surr}\), will have the opposite sign to \(q_{sys}\).
Express this relationship mathematically: \(q_{sys} = -q_{surr}\). This means if \(q_{sys}\) is positive (heat absorbed), then \(q_{surr}\) must be negative (heat lost).
Conclude that when a system absorbs heat from its surroundings, \(q_{sys}\) is positive and \(q_{surr}\) is negative, consistent with energy conservation and the First Law of Thermodynamics.
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