Idea 6of 9Builds onEnergy on the moveHow hot
The price per degree
Warming a kilogram of water one degree costs how much?
Today you'll discover
- what one degree costs, per kilogram
- why the same burner heats metal faster than water
- the number that prices a substance
Think firstEqual masses of water and aluminum on equal burners
Equal masses of water and aluminum on identical burners for one minute. Which is hotter?
Predict first, then drag the sliders. Watch the bill follow the mass and the rise.
A heating curve with the sloping piece highlighted and its slope triangle drawn: one hundred degrees for 420 kilojoules. After a prediction, the heat-bill bench opens with sliders for mass and temperature rise and a readout of the energy. The last step asks the energy to warm three kilograms of water by forty degrees.
See the whole ideathe big idea and the key word, in one place
The big idea
Each degree has a price per kilogram: Q = mcΔT.
Easy to get wrongUse the change in temperature, not the final reading. Warming from 20 to 60 is forty degrees' worth of bill, not sixty.
Key word
- specific heat capacity
- the energy needed to warm one kilogram of a substance by one degree: c, in J/(kg·°C); water's is 4200
About this modelDrawn to scale: boiling costs about seven times what melting costs, per kilogram.
Drawn to scale: boiling costs about seven times what melting costs, per kilogram.
Ready to use it?
- Find the energy to warm a given mass by a given number of degrees, with the substance's c.