O level Physics Heat Capacities

Terms

• Heat capacity is the amount of heat required to raise the temperature of a body by 1 K (or 1°C)
• Specific heat capacity is the amount of heat required to raise the temperature of 1kg of the substance by 1 K (or 1°C) 
• Latent heat of fusion of a solid substance is the heat energy needed to change it from solid to liquid state without any change in temperature 
• Specific latent heat of fusion of a solid substance is the heat energy needed to change 1kg of it from solid to liquid state without any change in temperature 
  • SI unit: J/kg 
• Latent heat of vaporisation of a substance is the heat energy needed to change it from liquid vapour state without any change in temperature 
• Specific latent heat of vaporisation of a substance is the heat energy needed to change 1kg of it from liquid to vapour state without any change in temperature 
  • SI unit: J/kg

 

 

Heat Change Formula

 

 

 

• Q = mcθ
  • m = mass (kg)
    c = specific heat capacity (J kg^{-1 o}C^-1)
    θ = temperature change (^o)

 

Electric heater

 

 

Energy Supply, E = Pt
Energy Received, Q = mcθ

 

Energy Supplied, E = Energy Receive, Q
Pt = mcθ

E = electrical Energy (J or Nm)
P = Power of the electric heater (W)
t = time (in second) (s)
Q = Heat Change (J or Nm)
m = mass (kg)
c = specific heat capacity (J kg^{-1 o}C^-1)
θ = temperature change (^o)

 

 

Mixing 2 liquids

Heat Gain by Liquid 1 = Heat Loss by Liquid 2
m₁c₁θ₁ = m₂c₂θ₂

m₁ = mass of liquid 1
c₁ = specific heat capacity of liquid 1
θ₁ = temperature change of liquid 1

m₂ = mass of liquid 2
c₂ = specific heat capacity of liquid 2
θ₂ = temperature change of liquid 2

Specific Latent Heat

Q = mL

Q = Heat Change (J or Nm)
m = mass (kg)
L = specific latent heat (J kg^-1)

 

1. A mass of 0.20kg of water at 0°C is placed in a vessel of negligible heat capacity. An electric heater with an output of 24 W is placed in the water and switched on. When the temperature of the water reaches 12°C, the heater is switched off.

a) Calculate the time for which the heater is switched on. Assume that the heat capacity of water is 4200J/kgK

b) An ice cube of mass 0.020kg is added to the 0.20kg of water at 0°C in the same vessel and the heater is switched on. Assuming that all the ice is at 0°C, calculate how long it will take for the water to reach 12°C. Assume that the specific latent heat of fusion on ice is 0.34 MJ/kg

Solutions

 

 

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