Thermodynamics & Heat Transfer · Heating a mass
The price of a degree
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The price of a degree

Warming something costs energy, and every material charges its own rate. The relation is Q=mcΔTQ = mc\Delta T — read aloud Q equals m c delta T. QQ is the heat added or removed, in kilojoules. mm is the mass being heated, in kilograms. cc is the specific heat capacity, in kJ/(kg·K) — the energy one kilogram needs for one kelvin of rise, and a property of the material, not of your process. And ΔT\Delta T is the temperature change in kelvin, never a temperature the substance sits at. That distinction is worth a mark on every paper you will ever sit.

This is sensible heat: the kind a thermometer can sense. Put it in and the reading climbs; take it out and the reading falls. Water's cc is about 4.2 kJ/(kg·K), which is enormous — a third more than glycol, eight times steel — and that single number is why the world moves heat around buildings and plants in water rather than in anything else.

The relation solves four ways, and a good exam will ask for all of them: m=QcΔTm = \dfrac{Q}{c\,\Delta T} when a heat meter tells you how much you warmed, c=QmΔTc = \dfrac{Q}{m\,\Delta T} when a calorimeter is identifying a fluid, and ΔT=Qmc\Delta T = \dfrac{Q}{mc} when you know the duty and want the rise. Run the units through each one: kJ divided by (kJ/(kg·K) × K) leaves kilograms, and every term that belongs on the bottom is on the bottom.