Mixing hot and cold: the method of mixtures
Pour hot water, or drop a hot block of iron or aluminium, into cold water and read the final temperature. Change the masses and temperatures and find the heat passed.
Core concept
When a hot body and cold water are mixed, heat flows until both reach one temperature, and the heat lost by the hot body equals the heat gained by the water: m₁c₁(T₁ − T) = m₂c₂(T − T₂)
Topic: Heat
Heat is energy: What is needed to make things move, heat up, light up or grow. All key words that flows from a hotter body to a colder one; temperature: How hot or cold something is, measured in degrees Celsius (°C). All key words tells how hot a body is. When hot and cold are mixed in an insulated container, heat flows until both reach the same final temperature (thermal equilibrium). If no heat escapes, the heat lost by the hot body equals the heat gained by the cold one: this is the principle of calorimetry, or the method of mixtures. The heat for a temperature change is Q = m × c × ΔT, where c is the specific heat capacity: 4200 J/kg°C for water, 900 J/kg°C for aluminium and 460 J/kg°C for iron. So heating 1 kg of water by 1 °C needs 4200 J, but 1 kg of iron needs only 460 J. In this lab the cold water always starts at 20 °C.
What you will learn
- State the principle of the method of mixtures.
- Calculate the final temperature of a mixture.
- Use Q = mcΔT to find the heat passed.
- Explain why water is used to cool engines and keep heat in hot-water bags.
Before you start
- Know the meaning of specific heat capacity.
Materials
- Hot and cold water, small blocks of iron and aluminium
Equipment
- A calorimeter or an insulated cup, two thermometers, a balance
Procedure
- Mix 100 g of water at 80 °C with 100 g of cold water, and record.
- Record with 200 g and 300 g of cold water.
- Record with the hot water at 100 °C.
- Record with a 100 g block of iron and of aluminium at 80 °C.
How this simulation is simplified
- No heat is lost to the container or the air.
- Specific heat capacities: water 4200, aluminium 900 and iron 460 J/kg°C.
- The cold water is at 20 °C.