Latent heat Specification references: P3.2.3 Changes of heat and specific latent heat M1a, M3b, M3c, M3d, M4a Aims In this worksheet, you will work through two worked examples designed to allow you to improve your maths skills. The focus is on solving algebraic equations, by substituting numbers into the equation and rearranging if needed. Learning outcomes After completing this activity you should be able to: identify when to use latent heat of fusion and latent heat of vaporisation apply the equation for latent heat substitute numerical values into algebraic equations using appropriate units solve algebraic equations. Setting the scene In this worksheet, you will be using the following equation: Thermal energy for a change in state (J) mass (kg) specific latent heat (J/kg) Useful values: Latent heat of vaporisation Substance Latent heat of fusion (J/kg) (J/kg) water 334 000 2 260 000 oxygen 14 000 210 000 silver 88 000 2 300 000 This resource sheet may have been changed from the original. 1
Worked examples 1 Calculate the energy released when 100 g of steam condenses. Step 1: Identify what you know and convert to standard units Mass 100 g 0.1 kg Since it is a change of state between gas and liquid you will need to use the latent heat of vaporisation. Latent heat of vaporisation 2 260 000 J/Kg Step 2: Substitute the numbers into the equation Energy required mass specific latent heat of vaporisation 0.1 2 260 000 226 000 J 2 Calculate the mass of ice lost from an iceberg melting, if the energy supplied was 835 000 000J. Step 1: Identify what you know and convert to standard units Energy 835 000 000J Since it is a change of state between a solid and a liquid, you will need to use the latent heat of fusion. Latent heat of fusion 334 000 J/Kg Step 2: Substitute the numbers into the equation Energy required mass specific latent heat 835 000 000 J mass 334 000 Step 3 Rearrange the equation to make mass the subject of the equation. Divide both sides of the equation by 334 000 835000000 mass 334000 334000 334000 2500 kg mass This resource sheet may have been changed from the original. 2
Questions 1 Before freezers and fridges, people used to buy ice to keep their food cool. The very rich even filled a special building called an icehouse to make sure they had ice throughout the summer. Calculate how much energy is required to melt a a 10 kg block of ice, b a 1000 kg block of ice. 2 A jeweller melts 500 g of silver to pour into a mould. Calculate how much energy was released as the silver solidified. 3 A container has 200 g of liquid oxygen in it. Calculate how much energy will be required to evaporate all the oxygen, assuming it is at its boiling point. 4 A kettle fails to switch off and boils for 5 minutes, wasting 600 000 J of energy. Calculate the mass of water lost during this time. (3) This resource sheet may have been changed from the original. 3
5 A student takes measurements to determine the latent heat of vaporisation of ethanol. They discover it takes 8460 J to evaporate 10 g from boiling point. Calculate the latent heat of vaporisation of ethanol. (3) 6 Calculate the mass of water you could evaporate from its boiling point with the energy required to melt 800 g of silver from its melting point. (5) This resource sheet may have been changed from the original. 4
Answers 7 Energy mass latent heat of fusion a Energy 10 334 000 Energy 3 340 000 J b Energy 1000 334 000 Energy 334 000 000 J 8 Energy mass latent heat of fusion Energy 0.5 88 000 Energy 44 000 J 9 Energy mass latent heat of vaporisation Energy 0.2 210 000 Energy 42 000 J 10 Energy mass latent heat of vaporisation 600 000 mass 2 260 000 600 000 Mass 2 260 000 Mass 0.3 kg to 1 dp (0.265) 11 Energy mass latent heat of vaporisation 8460 0.01 latent heat 8460 Latent heat 0.01 Latent heat 846 000 J/kg 12 Energy required to melt silver: Energy mass latent heat of fusion Energy 0.8 88 000 Energy 70 400 J Mass of water that can be evaporated: Energy mass Latent heat of vaporisation 70 400 mass 2 260 000 70 400 Mass = 2 260 000 Mass 0.031 kg This resource sheet may have been changed from the original. 5