Specific Heat — Q = mcΔT

The specific heat formula Q = mcΔT explained: heat, mass and temperature change, why water's value is huge, and a worked example.

What it means

Specific heat measures thermal stubbornness: how much heat a kilogram of material soaks up per degree of warming. Water's value (4186 J/(kg·°C)) is extraordinarily high — metals need roughly ten times less heat for the same temperature rise, which is why a metal spoon in hot soup burns you while the soup itself is merely hot. The equation is linear, so twice the mass or twice the temperature change needs twice the heat. Note that ΔT is identical in kelvin and degrees Celsius, so either scale works here.

Variables

Assumptions

• Specific heat c is constant over the temperature range
• No phase change occurs during heating
• No heat is lost to the surroundings

Derivation

Specific heat is defined as the heat required per unit mass per degree of temperature change: $c = Q/(m\Delta T)$. Rearranging the definition gives $Q = mc\Delta T$. It is a material property, measured by calorimetry.

Worked example

Given:

• m = 0.5 kg of water
• c = 4186 J/(kg·°C)
• ΔT = 80 − 20 = 60 °C

1. Write the formula: $Q = mc\Delta T$

2. Find the temperature change: $\Delta T = 80 - 20 = 60\ \mathrm{K}$

3. Substitute: $Q = 0.5 \times 4186 \times 60$

4. Multiply: $Q = 2093 \times 60 = 125{,}580\ \mathrm{J}$