Heat & Calorimetry
Heat and Calorimetry
Heat always flows from a hotter object to a colder one, never the other way, until both reach the same temperature. How much energy that takes depends on three things: how much stuff you're heating, what it's made of, and how big a temperature change you want.
The formula
Q = m · c · ΔT
- Q — heat energy (J): the energy transferred into or out of an object as heat
- m — mass (kg): how much of the substance is being heated or cooled
- c — specific heat (J/(kg·K)): the energy needed to raise one kilogram of the material by one kelvin
- ΔT — temperature change (K): the difference between the final and initial temperature
Worked example
How much heat energy is needed to warm 2 kg of water by 5 kelvin? (specific heat of water ≈ 4000 J/(kg·K))
- m = 2 kg
- c = 4000 J/(kg·K)
- ΔT = 5 K
- Q = m · c · ΔT
- Q = 2 kg × 4000 J/(kg·K) × 5 K
Q = 40,000 J
Test yourself
Instead of 2 kg, you now have 4 kg of water and still want to raise it by 5 kelvin. How much heat energy is needed?
- 40,000 J
- 160,000 J
- Correct answer: 80,000 J
Right! Doubling the mass doubles the energy needed: 4 kg × 4000 J/(kg·K) × 5 K = 80,000 J.
Back to the 2 kg of water, but now you want to raise its temperature by 10 kelvin instead of 5. How much heat energy is needed?
- Correct answer: 80,000 J
- 40,000 J
- 20,000 J
Exactly — doubling the temperature change doubles the energy: 2 kg × 4000 J/(kg·K) × 10 K = 80,000 J.
Where you see this
On the same afternoon, beach sand scorches your feet while the ocean stays cool — a kilogram of water swallows about 4000 joules per kelvin, several times what the sand needs, so the sea warms slowly all season. A metal spoon in hot soup shows the other side: low specific heat, fast temperature swing.
Common mistakes
The deepest confusion is heat and temperature as the same thing — temperature is how fast molecules move on average, heat is energy in transit, and the exchange rate between them is what this law states: Q = m · c · ΔT. Then watch the proportionality: doubling the mass doubles the energy (2 kg × 4000 J/(kg·K) × 5 K = 40,000 J becomes 80,000 J at 4 kg), and so does doubling the temperature change. Different materials genuinely pay different rates.
How it connects
The ideal gas law told you how a gas's temperature sets its pressure; this is the price list for changing temperature at all — mass, material, and change, multiplied out. Heat engines, next, try to run that heat flow through a cycle and extract work from it, and they will care deeply about how much heat they had to spend.