Idea 7of 9Builds onThe price per degree
What one loses, the other gains
Hot water meets cold water. Where does it settle?
Today you'll discover
- where two mixed temperatures settle, and why not always midway
- the one rule that balances the two bills
- how a hot block in cold water is priced
Think firstHot water poured into cold water in an insulated cup
Mix 1 kg of water at 80 °C with 1 kg at 20 °C in an insulated cup. Final reading?
Predict first, then press Next. Watch energy leave one side and arrive at the other.
A hot body and a cold body in contact, drawn as the spoon in the bowl, with the energy's path between them. After a prediction, the hot side is picked out losing energy, then the cold side gaining the same energy, then the rule is named. The last step asks which of a hot steel block and cold water changes temperature more.
See the whole ideathe big idea and the key word, in one place
The big idea
What the hot one loses, the cold one gains.
For exampleEqual masses of water: they meet half way. A small hot block in a lot of water: the block drops a long way and the water barely rises.
Key word
- heat exchange
- in an insulated system, the thermal energy lost by the hotter body equals the energy gained by the colder: m c ΔT (lost) = m c ΔT (gained)
About this modelParticles are drawn far apart and the arrows show energy, not matter, except in the convection loop where the fluid itself moves.
Particles are drawn far apart and the arrows show energy, not matter, except in the convection loop where the fluid itself moves.
Ready to use it?
- Find the final temperature when two known masses at known temperatures are mixed.