Specific Heat Capacity

Specific heat capacity (c) — the energy required to raise the temperature of 1 kg of a substance by 1 K, without a change of state. Its unit is J kg⁻¹ K⁻¹.

E = mcΔθ

The word specific means "per kilogram". A temperature change of 1 K is identical in size to a change of 1 °C, so a value of c is the same whichever of the two you use — but only for a change in temperature, never for an absolute one.

Example: water has an unusually high specific heat capacity, about 4180 J kg⁻¹ K⁻¹. This is why coastal areas have milder winters than places inland: the sea takes a great deal of energy to cool by even a small amount, and releases that energy slowly.

Measuring c by electrical heating — an insulated block of known mass is heated by an electrical heater while its temperature is monitored. The energy supplied is found from E = VIt, and c is calculated from the temperature rise. Plotting temperature against time and taking the gradient is better than using a single pair of readings, because it averages out fluctuations and makes any anomalies visible.

Why measured values come out too high — some of the energy supplied escapes to the surroundings rather than heating the block, so the measured temperature rise is smaller than it should be for the energy supplied. Since c = E / (mΔθ), too small a value of Δθ gives too large a value of c. Lagging the block, starting below room temperature and finishing an equal amount above it, all reduce this error.

Method of mixtures — a hot object of known mass and temperature is dropped into a liquid of known mass and temperature, and the final temperature recorded. Assuming no losses, the energy lost by the hot object equals the energy gained by the liquid.