SHC / SLH, Method of Mixtures

Objectives

Lesson outcomes

Define and use specific heat capacity in calculations involving temperature change.
Define and use specific latent heat for changes of state without temperature change.
Distinguish between specific latent heat of fusion and specific latent heat of vaporisation.
Apply conservation of energy to method-of-mixtures problems.

Syllabus

CIE 9702 syllabus points

2 linked

14.3.1 define and use specific heat capacity
14.3.2 define and use specific latent heat and distinguish between specific latent heat of fusion and specific latent heat of vaporisation

Definitions

Required definitions

Specific heat capacity
the energy required per unit mass per unit temperature rise.
Specific latent heat
the energy required per unit mass to change state without a change in temperature.
Specific latent heat of fusion
the energy required per unit mass to change between solid and liquid without a change in temperature.
Specific latent heat of vaporisation
the energy required per unit mass to change between liquid and gas without a change in temperature.

Lesson Notes

Student guidance and lesson notes

Overview

This lesson focuses on thermal energy calculations. You use specific heat capacity when a substance changes temperature, specific latent heat when a substance changes state, and conservation of energy when hot and cold materials are mixed.

What You Need to Know

Use specific heat capacity when the temperature changes without a change of state.
Use E = mc delta theta when the temperature changes and no change of state is taking place.
Use specific latent heat when state changes without a temperature change.
Use E = mL during melting, freezing, boiling, or condensing.
In method-of-mixtures questions, energy lost by the hotter part is equal to energy gained by the cooler part, after allowing for any stated losses or container effects.

How to Work Through It

Identify whether the process is a temperature change, a change of state, or a mixture.
Write the relevant energy term for each part of the system.
Use signs or clear words to separate energy lost from energy gained.
Check units carefully: c is in J kg^-1 K^-1 and L is in J kg^-1.

Check Your Understanding

Why does temperature stay constant during a change of state even though energy is still being transferred?
When should you use E = mc delta theta rather than E = mL?
In a mixture question, which object loses energy and which object gains energy?

Common Mistakes

Using E = mc delta theta during a change of state.
Forgetting to convert grams to kilograms before substituting values.
Assuming all mixtures reach the average of the starting temperatures.
Ignoring the thermal energy gained by the container when the question includes it.

Next Steps

Practise setting out energy-balance equations clearly.
Carry conservation of energy and kelvin-scale thinking into the ideal gas model.