Question 4 of 4 · Thermodynamic Systems and Energy · Advanced · About 20 min

Two-metal thermal equalisation

A thermally insulated enclosure contains a $1.40\,\mathrm{kg}$ metal insert at $85.0^\circ\mathrm{C}$ and a $2.60\,\mathrm{kg}$ metal sleeve at $22.0^\circ\mathrm{C}$ . Their constant specific heats are $0.900$ and $0.490\,\mathrm{kJ/(kg\,K)}$ , respectively. They are put into perfect thermal contact. Determine the common equilibrium temperature and the magnitude of heat transferred between the objects.

Two solid bodies exchange heat inside one insulated enclosure. — Schematic, not to scale unless dimensions are given.

Given

Insert mass 1.40 kg and heat capacity 0.900 kJ/(kg K)
Sleeve mass 2.60 kg and heat capacity 0.490 kJ/(kg K)
Initial temperatures 85.0 C and 22.0 C

Find

Equilibrium temperature
Magnitude of energy exchanged

Assumptions

No heat escapes the insulated assembly.
No phase change, work or temperature-dependent heat capacity.

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Two-metal thermal equalisation

Given

Find

Assumptions

Worked solution