Specific Heat Capacity v Specific Latent Heat

Specific Heat Capacity

Specific heat capacity is the amount of energy needed to raise the temperature of 1 kilogram of a substance by 16C (or 1 K). It depends on the material because different substances require different amounts of energy to increase their temperature.

The formula to calculate the energy transferred when heating a substance is:

$$Q = m \times c \times \Delta T$$

• Q = energy transferred (joules, J)
• m = mass of the substance (kilograms, kg)
• c = specific heat capacity (joules per kilogram per degree Celsius, J/kg6C)
• $\Delta T$ = change in temperature (in 6C or K; the size of one degree is the same in both scales)

For example, if you heat 2 kg of water (specific heat capacity approximately 4200 J/kg6C) from 206C to 306C, the energy transferred is:

$$Q = 2 \times 4200 \times (30 - 20) = 2 \times 4200 \times 10 = 84,000 \text{ J}$$

Specific Latent Heat

Specific latent heat is the amount of energy needed to change the state of 1 kilogram of a substance without changing its temperature. This energy is used to break or form bonds between particles during a phase change (such as melting or boiling). During phase changes, energy is used to overcome intermolecular forces rather than increasing the temperature.

During a phase change, the temperature remains constant even though energy is being transferred.

The formula to calculate the energy transferred during a phase change is:

$$Q = m \times L$$

• Q = energy transferred (joules, J)
• m = mass of the substance (kilograms, kg)
• L = specific latent heat (joules per kilogram, J/kg)

There are two main types of specific latent heat:

• Specific latent heat of fusion: energy needed to change 1 kg of a solid into a liquid (melting) or vice versa (freezing). For example, water's latent heat of fusion is about 334,000 J/kg.
• Specific latent heat of vaporisation: energy needed to change 1 kg of a liquid into a gas (boiling) or vice versa (condensing). For example, water's latent heat of vaporisation is about 2,260,000 J/kg.

Differences Between Specific Heat Capacity and Specific Latent Heat

Property	Specific Heat Capacity	Specific Latent Heat
Energy used for	Raising the temperature of a substance	Changing the state (phase) of a substance
Temperature change	Temperature changes (increases or decreases)	No temperature change during phase change
Formula	$Q = m \times c \times \Delta T$	$Q = m \times L$
Units of constant	J/kg6C	J/kg
Depends on	Material and temperature change	Material and type of phase change (fusion or vaporisation)

In summary, specific heat capacity relates to how much energy is required to change the temperature of a substance, while specific latent heat relates to the energy required to change its state without changing temperature.

For example, heating 1 kg of ice from -106C to 06C requires energy calculated using specific heat capacity. But melting that 1 kg of ice at 06C to water at 06C requires energy calculated using specific latent heat of fusion.

Example: Calculate the energy needed to melt 0.5 kg of ice at 06C if the specific latent heat of fusion of ice is 334,000 J/kg.

Using the formula $Q = m \times L$:

$$Q = 0.5 \times 334,000 = 167,000 \text{ J}$$