specific latent heat

• Latent heat:


  The energy required for a substance to change its state.
• When a change of state occurs in a substance, the energy supplied changes the INTERNAL ENERGY (energy stored) in the substance but NOT the TEMPERATURE.


  • Because the energy is used to break the FORCES of attraction between molecules (which raises the potential energy of the substance).
  • rather than raising the temperature of the substance (which increases the molecules' kinetic energy).

  
• The SPECIFIC LATENT HEAT of a substance:

  The amount of energy required to change the state of 1kg of the substance with no change in temperature.
• energy for a change of state (J) = mass (Kg) x specific latent heat (J/Kg)
• When using the equation, there's TWO types of specific latent heat that can be used:

  • Specific Latent Heat of FUSION
  • Specific Latent Heat of VAPORISATION

  Use the correct type of SPECIFIC LATENT HEAT in calculations.
• 1. The question is asking for energy during melting, so use the specific latent heat of FUSION:

  Mass: 7800g $\div$ 1000 = 7.8kg

  Specific Latent Heat of fusion = 334000 J/kg

  Energy:

  • 7.8 x 334000 = 2605200 = 2.61 x 10^6 J

  
• b) The question is asking for energy during BOILING, so use the specific latent heat of VAPORISATION:

  Mass: 7800g $\div$ 1000 = 7.8kg

  Specific Latent Heat of vaporisation of water = 2.26 x 10^6 J/kg

  Energy:

  • 7.8 x 2.26 x 10^6 = 17628000 = 1.76 x 10^7 J

  
• Specific heat capacity: For when temperature changes for when state stays the same.

  • While

  Specific latent heat: For when temperature stays the same for when state changes.
• SPECIFIC LATENT HEAT:

  This energy is used for breaking or forming bonds during a state change, like:

  • water boiling to become steam
  • ice melting to become water.

  During this change, the temperature of the substance does NOT increase.
• As we heat up a substance:

  • the particles gain energy in their kinetic energy store & increase their internal energy
  • the temperature increases as well, only if there isn’t a change in state.
• Temperature:


  A measure of the average internal energy of all the particles in a substance.
• Specific latent heat of fusion:


  The energy required / released

  • when 1kg of a substance changes its state from a solid to a liquid (or vice versa)
  • with no change in temperature.
  • melting
  • freezing

  Units of $L_f^{ }$ = J/Kg

  
• Specific latent heat of vapourisation:


  The energy required / released

  • when 1kg of a substance changes its state from a liquid to a gas / vapour (or vice versa).
  • with no change in temperature.
  • boiling
  • evaporating
  • condensing

  Units of $L_v^{ }$= J/Kg

  
• Specific latent heat of $L_f^{ }/L_v^{ }$ (J/Kg) = Energy / E (J) $\div$ Mass / M (Kg)
• 2 kg of ice melts and becomes water.

  • The latent heat of fusion of ice is 334,000 J/kg.
  • How much energy did it take to melt the ice?

  668000J
• 0.4 kg of water at 100°C boils to become steam.

  • The latent heat of vaporisation of water is 2,260,000 J/kg.
  • How much energy did it take to boil the water?

  904000J
• A container has 200g of liquid oxygen.

  • Calculate how much energy will be required to evaporate all the oxygen, assuming it is at its boiling point.

  E = mLv

  • mass = 200g $\div$ 1000 = 0.2Kg
  • Specific latent heat of vaporisation = 210,000 J/Kg

  Energy required = 0.2Kg x 210,000 J/Kg = 42,000J
• A container has 200g of liquid oxygen.

  • Calculate how much energy will be required to evaporate all the oxygen, assuming it is at its boiling point.

  E = mLv

  • Mass = 200g / 1000 = 0.2Kg
  • Specific latent heat of vaporisation = 210,000J/Kg

  Energy required = 0.2Kg x 210,000J/Kg = 42000J
• A kettle fails to switch off and boils for 5 mins, wasting 600000 J of energy.

  • Calculate the mass of water lost during this time.

  E = mLv

  • mass = E / Lv
  • Energy required = 600,000 J
  • Specific latent heat of vaporisation = 2,260,000 J/Kg

  mass lost = 600,000 J $\div$ 2,260,000 J/Kg = 0.27 Kg (2 d.p.)
• Calculate the mass of water, you could evaporate from its boiling point with the energy required to melt 800g of silver from its melting point.

  First find out the energy required to turn solid silver to liquid silver:

  • E = mLf
  • mass = 800g / 1000 = 0.8Kg
  • Specific latent heat of fusion = 88000 J/Kg
  • Energy required = 0.8Kg x 88000 J/Kg = 70400 J

  Now find the mass of water, turning liquid water to water vapour

  • E = mLv
  • m = E / Lv
  • Energy required = 70400 J
  • Specific latent heat of vaporisation = 2,260,000 J/Kg

  Mass = 70400 J / 2,260,000 J/Kg = 0.031Kg
• • E = mL
  • m = E / L
  • L = E / M
• Total energy = energy of latent heat + energy of heat capacity

  • E = (m x L) + (m x c x Δθ)

  7436J = (0.02Kg x 334000J/Kg) + (0.02Kg x 2100J/Kg℃ x Δθ)

  • Find out change in temperature

  7436J = 6680J + (42 x Δθ)J

  • 7436J - 6680J = (42 x Δθ)J

  Δθ = (7436J - 6680J) $\div$ 42 = 18℃

  
• What happens to the temperature of nitrogen as it boils?

  stays the same
• • 165kJ x 1000 = 165000J

  Total internal energy = energy of SHC + energy of Lf

  • E = mcΔθ 
  • E = mLf

  Total energy = (mcΔθ) + (mLf)

  • 165000J  = (m x 3500J/Kg℃ x 21.5℃) + (m x 255000)
  • 165000J = (m x 75250) + (m x 255000)
  • 165000J = m x 330250

  Mass = 165000J / 330250

  • Mass = 0.50Kg (2 s.f.)