Thermal Energy Sharing
Thermal Energy Sharing
When objects reach one final temperature, energy lost by hotter parts equals energy gained by cooler parts—if no energy leaves the system.
Energy lost equals energy gained
A system does not exchange thermal energy with its surroundings. Use a separate energy term for every material.
Thermal Equilibrium Explorer
The two blocks are made from the same material. The cool block has a mass of 1.00 kg and starts at 20 °C. Change the hot block, then compare the final temperature with the simple midpoint.
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final temperature
50.0 °C
simple midpoint
50.0 °C
hot block share of total mass
50%
The midpoint works only when the two heat capacities are equal. In this model, both blocks are the same material, so changing the mass changes the heat capacity.
Key idea
Worked example
Energy is supplied to two joined blocks
A 0.54 kg copper block and a 0.37 kg aluminium block are joined and start at the same temperature. A heater supplies 24 kJ to the combined, isolated system. The specific heat capacities are shown below.
- Both blocks start together and finish together, so they have the same temperature rise.
- Add the energy received by the two blocks.CCu=0.54×390CCu=211 JK−1CAl=0.37×910CAl=337 JK−1Ctotal=548 JK−124000=548Δθ
- Calculate the common temperature rise.Δθ=43.8516 K
Adapted from (9702/42/F/M/25 Q3(a)(ii)).
Write one energy term for each material. The single supplied energy is shared by the whole system; do not give the full energy to every part.
A small hot block and a much larger cold block are made of the same material. They are placed together in an isolated container. Is the final temperature closer to the hot or cold starting temperature?
Show worked answer
It is closer to the cold starting temperature. The larger cold block has the larger thermal capacity, so the final temperature is not the simple midpoint.