Practice

Q = mcΔT Formula – Specific Heat Practice

Q = mcΔT — Heat for a temperature change (no phase change)

The heat needed to change a substance’s temperature (without a phase change) is Q = m c ΔT. Here c is specific heat capacity and ΔT = T₂ − T₁.

Guide — how to use this formula

1. 1. Convert mass to kilograms if c is in J/kg·°C.
2. 2. Compute ΔT = T₂ − T₁ (or use the given rise).
3. 3. Q = m c ΔT; rearrange for c, m, or ΔT as needed.
4. 4. Heater power: P = Q/t after finding Q.

Derivation

Specific heat c is defined so that heat is proportional to mass and temperature change:

1. Definition:
   Q = mc\Delta T
2. Average heating power over time t:
   P = \frac{Q}{t}

ΔT is the change — never substitute the final temperature alone.

Examples

Example: 1 kg water +10 °C

c = 4200 → Q = 42,000 J.

Example: find ΔT

Q = 84,000 J, m = 2 kg, c = 4200 → ΔT = 10 °C.

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