Mixum

Meet Mixum, a hot mug of water who shares her warmth with a cold one.

When a hot and a cold object touch inside an insulated container, energy flows from hot to cold until they reach the same temperature. If no energy escapes, the energy lost by one equals the energy gained by the other. That is what the minus sign in the equation means.

Mix 0.20 kg of water at 80 °C with 0.30 kg at 20 °C. Both have the same specific heat, 4186 J/(kg·K), so the final temperature is (0.20 × 80 + 0.30 × 20) / 0.50 = 44 °C. The hot water cools by 36 K, and the cold water warms by 24 K.

Specific heat depends on the material. Water has one of the highest of common substances, while iron is about 450 J/(kg·K), so a hot iron nail dropped into a cup of water barely warms it.

In the 1760s, Joseph Black used experiments like this to separate the ideas of temperature and heat. Calorimeters are still used to measure the energy in foods and fuels.