3.1.5 Specific Latent Heat

• During a phase change (i.e. a change of state) thermal energy is transferred to a substance or removed from it, while the temperature of the substance does not change
• In this case, the thermal energy is calculated as follows:

E = mL

• Where:
  • m = mass of the substance in kilograms (kg)
  • L = specific latent heat of the substance in J kg^–1

• The specific latent heat of a substance is defined as:

The amount of energy required to change the state of 1 kg of a substance without changing its temperature

• This definition can be explained when the above equation is rearranged for L:

• This means that the higher the specific latent heat of a substance, the greater the energy needed to change its state
  • Note that the specific latent heat is measured in J kg^–1

• The amount of energy required to melt (or solidify) a substance is not the same as the amount of energy required to evaporate (or condense) the same substance
• Hence, there are two types of specific heat:
  • Specific latent heat of fusion, L_f
  • Specific latent heat of vaporisation, L_v

• Specific latent heat of fusion is defined as:

The amount of energy needed to melt or solidify a material at its melting point

• This applies to the following phase changes:
  • Solid to liquid
  • Liquid to solid

• Specific latent heat of vaporisation is defined as:

The amount of energy needed to evaporate or condense a material at its boiling point

• This applies to the following phase changes:
  • Liquid to gas
  • Gas to liquid

• For the same substance, the value of the specific latent heat of vaporisation is always much higher than the value of the specific latent heat of fusion
  • In other words, L_v > L_f

• This is because much more energy is needed to evaporate (or condense) a substance than it is needed to melt it (or solidify it)

Step 1: Determine whether to use latent heat of fusion or vaporisation

• • We need to use the specific latent heat of fusion because the phase change occurring is from solid to liquid

Step 2: List the known quantities

• • Mass of the ice, m = 200 g = 0.2 kg
  • Specific latent heat of fusion of water, L_f = 3.3 × 10⁵ J kg^–1

Step 3: Write down the equation for the thermal energy 

E = mL_f

Step 4: Substitute numbers into the equation 

E = 0.2 kg × (3.3 × 10⁵) J kg^–1

 = 6.6 × 10⁴ J = 66 kJ

Step 1: Determine whether to use latent heat of fusion or vaporisation

• • We need to use the specific latent heat of vaporisation because the phase change occurring is from liquid to gas

Step 2: Write down the known quantities

• • Power, P = 2500 W
  • Mass, m = 0.50 kg
  • Specific latent heat of vaporisation of water, L_v = 2.3 × 10⁶ J kg^–1

Step 3: Recall the equation linking power P, energy E and time t

E = Pt

Step 4: Write down the equation for the thermal energy E 

• • The energy E in the previous equation is the thermal energy transferred by the heater to the water

E = mL_f

Step 5: Equate the two expressions for energy 

Pt = mL_f

Step 6: Solve for the time t 

t = 460 s