Latent Heat and State Changes
This topic covers how the state of matter changes (e.g., solid to liquid) and the energy required for these transitions. It focuses on the concept that during a state change, temperature remains constant while energy, known as latent heat, is absorbed or released.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- During a change of state, the temperature of a pure substance does not change, even though thermal energy is being supplied or removed.
- The energy supplied during a state change alters the potential energy of the molecules by changing the bonds between them, not their kinetic energy.
- On a temperature-time graph for a substance being heated at a constant rate, the flat sections (plateaus) represent changes of state occurring at the melting and boiling points.
- Melting (solid to liquid) and boiling (liquid to gas) are processes that absorb energy from the surroundings.
- Freezing (liquid to solid) and condensing (gas to liquid) are processes that release energy to the surroundings.
- For most substances, the specific latent heat of vaporisation is significantly larger than the specific latent heat of fusion.
Diagram
› Why does this happen?
Why does temperature stay constant during a state change?
Temperature is a measure of the average kinetic energy (the movement energy) of the particles in a substance. When you heat a solid, its particles vibrate more, their kinetic energy increases, and so the temperature rises. However, when the substance reaches its melting point, the extra energy supplied is used for a different job. Instead of making the particles move faster, this energy is used to weaken the forces of attraction holding the particles in their fixed positions. This increases their potential energy, not their kinetic energy. Because the average kinetic energy isn't changing, the temperature stays constant until all the solid has melted. A similar thing happens at the boiling point. Here, the energy is used to overcome the forces between liquid particles completely so they can escape as a gas.
Why is more energy needed for boiling than for melting?
This is all about how much the forces between particles need to be overcome. During melting, you are only weakening the strong forces between particles enough to let them break out of their fixed positions and slide past each other. The particles in a liquid are still very close together. During boiling, you have to do much more work. You need to provide enough energy to overcome the forces of attraction between particles completely, allowing them to separate and move far apart to form a gas. Because completely separating the particles requires much more energy than just loosening them, the specific latent heat of vaporisation is significantly larger than the specific latent heat of fusion for most substances.
Formulae
E = m × L To calculate the thermal energy (E) needed to change the state of a mass (m) of a substance. Use the specific latent heat of fusion (Lf) for melting/freezing, or vaporisation (Lv) for boiling/condensing.
Definitions
- Melting Point
- The specific, constant temperature at which a pure substance transitions from a solid to a liquid.
- Boiling Point
- The specific, constant temperature at which a pure substance transitions from a liquid to a gas.
- Specific Latent Heat of Fusion (L_f)
- The amount of energy required to change 1 kg of a substance from solid to liquid without any change in temperature.
- Specific Latent Heat of Vaporisation (L_v)
- The amount of energy required to change 1 kg of a substance from liquid to gas without any change in temperature.
Worked example
It takes 66,000 J of energy to completely melt a 200 g block of a pure substance initially at its melting point. What is the specific latent heat of fusion of the substance in kJ/kg?
- 1
Identify the formula to rearrange:
E = m × L, so L = E / m - 2
Ensure all units are in standard SI form for the calculation.
Mass m = 200 g = 0.2 kgEnergy E = 66,000 J - 3
Substitute the values into the rearranged formula:
L = 66,000 J / 0.2 kg - 4
To divide by 0.2, it's easier to multiply the top and bottom of the fraction by 10 to remove the decimal:
L = 660,000 J / 2 kg - 5
Perform the division:
L = 330,000 J/kg - 6
Convert the final answer to kJ/kg as requested by the question:
330,000 J/kg = 330 kJ/kg.
Answer: 330 kJ/kg
Common mistakes
- ×Making arithmetic errors with large numbers and decimals, especially when converting between J and kJ or g and kg.
- ×Forgetting to convert mass from grams to kilograms before using the formula. The standard unit for specific latent heat is J/kg, so mass must be in kg.
- ×In multi-step problems that also involve temperature changes, confusing the specific heat capacity formula (E=mcΔT) with the specific latent heat formula (E=mL).
No-calculator tips
- ✓Convert all prefixes like 'kilo' (103) and units like grams (10-3 kg) into powers of 10 at the beginning. This turns complex multiplication/division into simple addition/subtraction of indices.
- ✓To divide by a decimal like 0.2, multiply both the numerator and denominator by 10 (making it a division by 2). To divide by 0.05, multiply by 100 (making it a division by 5).
- ✓Break down large numbers. For example, calculating 0.2 × 330,000 can be thought of as (2 × 330,000) / 10, which is 660,000 / 10 = 66,000.