Heat is energy in transit
In everyday speech 'heat' means anything warm, but in physics heat has one precise meaning: energy that flows from one body to another because of a temperature difference. Heat is not a substance stored inside an object. What an object stores is thermal energy — the total kinetic (and potential) energy of its jiggling molecules. Heat is what we call that energy while it is crossing the boundary from hot to cold.
Why the same flame warms different things differently
Give equal amounts of heat to a kilogram of water, a kilogram of cooking oil, and a kilogram of iron. The iron shoots up in temperature, the oil less so, the water barely warms. Each material has its own resistance to being heated, captured by its specific heat capacity c: the heat needed to raise one kilogram by one kelvin. The relation is one of the workhorse equations of thermal physics.
Heat to change a mass m by a temperature ΔT (no phase change). Q > 0 means heat added; Q < 0 means heat removed.
Water's specific heat, about 4186 J·kg⁻¹·K⁻¹, is remarkably large — far bigger than metals (iron ≈ 450, aluminum ≈ 900). This single fact explains a lot of the world: coastal towns have milder weather than inland ones because the sea stores and releases heat sluggishly; car engines and power plants use water as a coolant; and your body, mostly water, resists overheating. A big c means a big thermal buffer.
Heat capacity and molar heat capacity
Sometimes we care about a whole object rather than a per-kilogram figure. The heat capacity C = mc is the heat that particular object needs per kelvin. A cast-iron pan and a thin steel spoon are the same metal (same c) but the heavy pan has a far larger heat capacity, so it takes longer to heat and holds warmth longer. When we count by molecules instead of mass we use the molar heat capacity, the heat per mole per kelvin — the natural unit once we reach gases and the kinetic theory.
Heat capacity C is specific heat times mass; it applies to one specific object.
Calorimetry: energy bookkeeping when hot meets cold
Drop a hot lump of metal into cool water in a well-insulated cup and wait. Heat leaves the metal and enters the water until both reach one final temperature T_f. If no energy escapes to the surroundings, then the energy is conserved: every joule the metal loses, the water gains. This accounting is calorimetry, and writing it down is just insisting that the heats sum to zero.
The calorimetry equation: with each Q written as mcΔT (final minus initial), the heat lost by the hot body plus the heat gained by the cold body is zero.
Worked example: find the final temperature
- 0.50 kg of aluminum at 200 °C is dropped into 1.0 kg of water at 20 °C in an insulated container. Use c(Al) = 900 J·kg⁻¹·K⁻¹ and c(water) = 4186 J·kg⁻¹·K⁻¹. Find the final temperature T_f.
- Set heat lost + heat gained = 0: (0.50)(900)(T_f − 200) + (1.0)(4186)(T_f − 20) = 0.
- Expand: 450·T_f − 90000 + 4186·T_f − 83720 = 0, so 4636·T_f = 173720.
- T_f = 173720 / 4636 ≈ 37.5 °C. Sanity check: the answer sits between 20 and 200 °C, and lands much closer to the water's 20 °C — because water's m·c (4186) hugely outweighs the aluminum's (450), so the water 'wins' the tug-of-war over the final temperature.