Upper secondary · 15 min

Measuring heat with a coffee-cup calorimeter

Drop a hot metal block into water inside an insulated cup and deduce the metal’s specific heat from q = mcΔT.

Goal

Use q = mcΔT for both the water and the metal, and extract the metal’s specific heat capacity from the measured ΔT.

Apparatus and reagents

Insulated foam cup, thermometer, balance, 50 g of water, and ~25 g blocks of Al, Cu and Pb heated in a water bath.

Procedure

Weigh 50 g of water into the insulated cup and record its temperature, T₁ = 25.0 °C.
Heat a 25 g metal block to about 95 °C in a water bath, then transfer it quickly into the cup.
Stir gently and read the highest steady temperature T₂.
Repeat for the other metals and compare the ΔT values.

What to observe

The temperature rise differs strongly between metals: Al warms the water ≈ 7.5 K, Cu ≈ 3.3 K and Pb only ≈ 1.1 K for the same mass and initial temperature.
The thermometer shows a fast rise then a plateau — the thermal equilibrium where the heat lost by the metal equals the heat gained by the water.

Explanation

With heat losses neglected, q_metal = −q_water, so m_metal·c_metal·(T₂−95) = −m_water·c_water·(T₂−25). Solving for c_metal recovers 0.90, 0.39 and 0.13 J g⁻¹ K⁻¹ for Al, Cu and Pb: a small specific heat means the same mass stores less thermal energy. In a real cup a few percent of the heat escapes or is absorbed by the cup itself, so measured ΔT runs slightly low.

History of the experiment

Joseph Black introduced specific and latent heats around 1760 by tracking how ice and water exchange heat. Lavoisier and Laplace built the first ice calorimeter in 1782 to measure animal heat and combustion. Coffee-cup calorimetry remains the simplest classroom version of those ideas.

Chemists behind it

Joseph Black