Specific heat — Q = mcΔT
What we'll do: We'll heat different substances with the same portion of heat and check how much their temperature rises — and mix bodies together, calculating the final temperature.
What you see on screen: Vessels with substances, a heater and thermometers, plus sliders for mass, specific heat and supplied heat; bars show Q, m, c and the temperature rise. Readouts: substance, specific heat, mass, supplied heat, temperature rise and (in balance mode) the final temperature.
I will give you a target temperature rise — pick the substance, mass and heat (Heating mode) to reach it. Q = m·c·ΔT.
What just happened?
The same portion of heat warmed the oil more than the water — because oil has a smaller specific heat. Water is harder to heat up.
What is specific heat?
It is the amount of energy needed to heat 1 kilogram of a substance by 1 kelvin (or 1°C). Unit: J/(kg·K). Every substance has its own value — water a large one (4200), metals a small one (e.g. iron ~450).
Formula:
Q — supplied heat, m — mass, c — specific heat, ΔT — temperature rise. Rearranging:
Why does water heat up slowly?
Because it has a very large specific heat — it needs a lot of energy to warm up and releases a lot as it cools. That is why seas moderate the climate and water is great at cooling engines.
Heat balance:
when you bring bodies of different temperatures into contact, the heat given off by the warmer one = the heat absorbed by the cooler one — until their temperatures equalise.
Why you need this for the exam:
calculations with Q = mcΔT and heat balance (mixing bodies, finding the final temperature or the specific heat) are calorimetry classics. Tip: watch the units and keep track of what is being asked for.
Remember: Q = mcΔT; the smaller the specific heat, the faster a substance heats up. Water has a large c, so it heats up and cools down slowly.
Theory & formulas
Heat needed to warm a body
The amount of heat needed to change a body's temperature:
Specific heat
is the amount of energy needed to heat of a substance by (in ). Water has a very large specific heat, which is why it heats up and cools down more slowly than metal.
Heat balance
When bodies are mixed, the heat given off by the warmer one equals the heat absorbed by the cooler one: From this you compute the common final temperature.
Symbols: — heat, — mass, — specific heat, — temperature rise.
Frequently asked questions
›What is specific heat?
The amount of energy needed to heat 1 kg of a substance by 1 K, expressed in J/(kg·K).
›How do you calculate the heat needed to warm a body?
From the formula Q = m·c·ΔT (mass × specific heat × temperature rise).
›Why does water heat up and cool down more slowly than metal?
Because it has a much larger specific heat — it needs more energy to change its temperature.
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