A thermally isolated system is made up of a hot piece of aluminum and a cold piece of copper; the aluminum and the copper are in thermal contact. The specific heat capacity of aluminum is more than double that of copper. Which object experiences the greater magnitude gain or loss of heat flow during the time the system takes to reach thermal equilibrium?

Question

BlackTom AI · Accepted Answer

To understand the heat transfer in this isolated two-object system, we start from the basic energy balance: the total heat leaving the hotter object must equal the total heat entering the cooler object, since no energy escapes the system.
Option 1: the aluminum. This would claim the aluminum loses a different amount of heat than the copper gains. That’s not correct for an isolated exchange between two bodies: the magnitude of heat transferred from one to the other is the same for both, just with opposite signs. So this option misstates the symmetry of heat exchange.
Option 2: the copper. Similarly, saying the copper experiences a greater loss or gain than the aluminum contradicts energy conservation in a closed pair of bodies exchanging heat; the copper’s heat gain equals the aluminum’s heat loss in magnitude.
Option 3: Neither; both experience the same size gain or loss of heat flow. This matches the fundamental principle that, during mutual heat exchange in an isolated system, the amount of heat lost by the hotter object equals the amount gained by the cooler object (Q_hot = -Q_cold) in magnitude, regardless of each object’s specific heat.
Option 4: It is impossible to tell without knowing the masses. While masses and specific heats determine the final temperatures and how much each object changes temperature, they do not change the fact that the amount of heat transferred between the two objects is equal in magnitude for both during the equilibration process. The masses influence ΔT via Q = m c ΔT, but not the equality of heat flow magnitudes between the two bodies.
Overall, the key concept is conservation of energy during heat exchange: the same amount of heat leaves the hot piece and enters the cold piece, so the magnitudes are equal for both objects.

SPHY001 Practice Quiz - Unit 14 | LA054

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