A 100 gram piece of heated iron cools from 50° to 20°C. How much heat is released to the surroundings?

Question

BlackTom AI · Accepted Answer

To assess the heat transfer for the iron piece, we start from the general relation Q = m c ΔT, where Q is the heat exchanged, m is mass, c is the specific heat capacity, and ΔT is the change in temperature.
Option 1: 300 J of heat are released. This would require a specific combination of mass, c, and ΔT that yields 300 J. Given m = 100 g and ΔT = 30°C, this would imply an average c around 0.01 J/g°C, which is far from the known values for iron. Thus this answer undervalues the heat release.
Option 2: 300 cal of heat are released. Converting 300 cal to joules gives about 1255 J. If we used Q ≈ 1255 J with m = 100 g and ΔT = 30°C, the implied c would be about 0.42 J/g°C, which is in the ballpark of iron’s typical specific heat, but the problem statement does not provide c in calories nor explicitly authorize using a conversion in this way. The mismatch between units and the given data makes this option unreliable without further clarification.
Option 3: The amount of heat cannot be calculated because the heat capacity is not known. This is a valid restriction: without a given c value for iron in the problem, you cannot compute a precise Q using Q = m c ΔT. Although one might recall a standard approximate c for iron from memory, the data as presented do not supply c, so a calculation cannot be completed strictly from the provided information.
Option 4: The amount of heat cannot be calculated because there is no closed system. The idea of a closed system matters for energy accounting, but calorimetry commonly treats the object and surroundings as the system and surroundings exchanging heat until thermal equilibrium. The lack of a closed system is not the reason you cannot compute Q from m, c, and ΔT given, so this justification is not correct in this context.
In summary, the only option that correctly points out the insufficiency of the given data for a numerical calculation is the one that cites the missing heat capacity (c) as the barrier to determining Q, since Q depends on c through Q = m c ΔT. This aligns with the need for a provided specific heat capacity to proceed with an exact numerical result.

A 100 gram piece of heated iron cools from 50° to 20°C. How much heat is released to the surroundings?单项选择题

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