# Specific Latent Heat ## Specific Latent Heat of Fusion & Vaporisation - Energy is required to change the **state** of a substance - Examples of changes of state include: - **Melting** = solid to liquid - **Evaporation/vaporisation/boiling** = liquid to gas - **Sublimation** = solid to gas - **Freezing** = liquid to solid - **Condensation** = gas to liquid

Latent heat is the thermal energy required to change the state of 1 kg of a substance without any change of temperature

- When a substance changes state, there is **no temperature change** - The energy supplied during a change of state is called the latent heat - There are two types of latent heat: - **Specific latent heat of fusion** (melting) - **Specific latent heat of vaporisation** (boiling) ### Specific Latent Heat of Fusion - The specific latent heat of fusion is used when a solid is melting or a liquid is freezing - It is defined as: **The thermal energy required to convert 1 kg of solid to liquid with no change in temperature** ### Specific Latent Heat of Vaporisation - The specific latent heat of vaporisation is used when a liquid is vapourising or a gas is condensing - It is defined as: **The thermal energy required to convert 1 kg of liquid to gas with no change in temperature** ### Energy Changes During Phase Transitions - During a change of state, **temperature remains constant** even though energy is being supplied - The energy goes into changing the **electrostatic potential energy** between molecules, not their kinetic energy - For melting: - Energy is required to increase the molecular separation until molecules can flow freely over each other - For vaporisation: - Energy is required to completely separate the molecules until there are no longer forces of attraction between them - This requires **much more energy** than melting #### Heating Curve for Water The graph below shows how the temperature of water changes as it is heated continuously from ice to steam. Notice the flat regions where phase changes occur:

- Between 2-4 minutes: Ice is melting at 0°C (fusion) - Between 8-18 minutes: Water is boiling at 100°C (vaporisation) - The flat sections show that temperature remains constant during phase changes - The vaporisation plateau is longer, reflecting the greater energy required ## Determining Specific Latent Heat - The amount of thermal energy $E$ required to melt or vaporise a mass $m$ with latent heat $L$ is: $$E = mL$$ - Where: - $E$ = amount of thermal energy to change the state (J) - $L$ = latent heat of fusion or vaporisation (J kg$^{-1}$) - $m$ = mass of the substance changing state (kg) - Specific latent heat of fusion is represented by $L_f$ - Specific latent heat of vaporisation is represented by $L_v$ ### Values for Water | **Change of State** | **Specific Latent Heat Value** | |---|---| | Fusion (ice to water) | 330 kJ kg$^{-1}$ | | Vaporisation (water to steam) | 2.26 MJ kg$^{-1}$ |

Evaporating 1 kg of water requires roughly seven times more energy than melting the same amount of ice

### Worked Example A laboratory experiment requires boiling 450 g of ethanol. If 0.42 MJ of energy is supplied to achieve this, calculate the specific latent heat of ethanol and identify whether this is fusion or vaporisation. **Step 1: State the known values** - Mass, $m = 450 \text{ g} = 0.45 \text{ kg}$ - Energy supplied, $E = 0.42 \text{ MJ} = 0.42 \times 10^6 \text{ J}$ **Step 2: State the specific latent heat equation** $$E = mL$$ **Step 3: Rearrange for latent heat** $$L = \frac{E}{m}$$ **Step 4: Substitute in the values** $$L = \frac{0.42 \times 10^6}{0.45} = 9.33 \times 10^5 \text{ J kg}^{-1} = 0.93 \text{ MJ kg}^{-1} \text{ (2 s.f.)}$$ **Step 5: Identify the type of latent heat** - $L$ is the latent heat of **vaporisation** because the change in state is from liquid to gas (boiling) ## Procedures to Determine Specific Latent Heat ### Determining the Specific Latent Heat of Fusion, $L_f$ #### Equipment List - Crushed ice - Two funnels with filter paper - Three retort stands - Two thermometers - Two electric balances - An appropriate heater (e.g., an immersion heater) - A power source - A voltmeter, ammeter and stop-clock #### Method 1. Place a beaker on each balance - Leaving the beaker on the balance, zero the scale 2. Arrange a funnel, clamped above each beaker 3. Set up an immersion heater - Connect to the power source - Add an ammeter in series and a voltmeter in parallel 4. Place the immersion heater in one of the funnels 5. Measure out 50-100 g of ice - Add the same mass of ice to each funnel - Record this value 6. Turn on the immersion heater and start the stop watch 7. Record the potential difference and current - Record these values 8. After a suitable period of time (around 5-10 minutes) remove the funnels, stop the stop watch and turn off the heater 9. Record the mass of water in each beaker #### Analysis - The energy supplied to the ice can be calculated using: $$\text{energy} = \text{current} \times \text{potential difference} \times \text{time}$$ - Using the values for current, potential difference and time, calculate the energy supplied - The specific latent heat of fusion can be calculated using: $$\text{energy} = \text{mass} \times \text{specific latent heat}$$ - To account for melting due to heat transfer from the surroundings, find the difference in mass between the two beakers: $$\Delta m = m_A - m_B$$ - This gives the change in mass due to the energy supplied by the heater - Convert the mass of melted ice into kg: $$\text{Mass in g} \div 1000 = \text{Mass in kg}$$ - Calculate the specific latent heat of fusion of ice using the rearranged equation: $$L_f = \frac{E}{\Delta m}$$ #### Evaluation - Errors may be introduced due to precision of the instruments - Water may be absorbed by the filter paper - This will reduce the measured mass and therefore give a higher value for specific latent heat ### Determining the Specific Latent Heat of Vaporisation, $L_v$ #### Equipment List - A double-walled glass vessel with an inner flask containing water - An appropriate electric heater (e.g., an immersion heater) - A condenser with a collecting flask - A power source - A voltmeter, ammeter and stop-clock - An electric balance #### Method 1. Connect the double-walled glass vessel to the condenser 2. Place the collecting flask at the end of the condenser 3. Set up an immersion heater - Connect to the power source - Add an ammeter in series and a voltmeter in parallel 4. Place the immersion heater in the fluid 5. Turn on the immersion heater and start the stop watch 6. Record the potential difference and current 7. After a suitable period of time (around 5-10 minutes), stop the stop watch and turn off the heater 8. Record the mass of water collected in the collecting flask #### Analysis - The energy supplied to the water can be calculated using: $$\text{energy} = \text{current} \times \text{potential difference} \times \text{time}$$ - Using the values for current, potential difference and time, calculate the energy supplied - The specific latent heat of vaporisation can be calculated using: - The mass of water collected - The energy supplied calculated - The equation: $$E = mL_v$$ - Rearrange to find $L_v$: $$L_v = \frac{E}{m}$$ #### Evaluation - Errors may be introduced due to precision of the instruments - Not all of the vapour which enters the condenser may make it to the collecting flask - Some condensation may remain on the walls of the condenser - This leads to a lower measured mass and a higher calculated value for specific latent heat

During a change of state, temperature remains constant even though the substance is being heated or cooled