10 Heat and Temperature

10 Heat and energy

Heat and temperature

If a hot body is brought into contact with a cold body, heat will be transferred from the hot body to the cold body. 

 In order to measure the quantity of heat, we must have a suitable heat unit.   

Heat is a form of energy and therefore has the same unit as any other form of energy, ie the joule (J).

Specific heat capacity

Specific heat capacity is defined as the amount of heat energy required to give unit mass of a substance a temperature rise of one degree.

For example, one kilogram of water requires 4187 joules (4.187kJ) of heat energy to raise its temperature by one degree Celsius.

Thus, the specific heat capacity of water is 4187 joules per kilogram per one degree Celsius.

This value is normally stated as 4187 J/kg°C.

The symbol used for specific heat capacity is ‘c’.

Specific heat capacities

This table gives typical values of the specific heat capacity, c, for various substances.

Quantity of heat energy

The amount or quantity of heat energy, Q, required to raise the temperature of a substance depends upon:

• The mass, m, of the substance—the larger the mass, the greater the heat energy required

• The specific heat capacity, c, of the substance

• The temperature change, Δt — the greater the change in temperature, the larger the quantity of heat energy required

Therefor:

Quantity of heat energy  =  mass x specific heat capacity x temperature change

or

Q  =  mcΔt

Δ is the symbol for change, therefore Δt means change in temperature.

The SI unit for quantity of heat is the joule (abbreviation J).

The units kilo joule (1 kJ  =  103 J) and mega joule (1 MJ = 106 J) are also used.

Example 1

Calculate the amount of heat, in mega joules, that is necessary to raise 5 kg of water from 20°C to 100°C.

Take the specific heat capacity of water to be 4187 J/kg°C 

Q  =  mcΔt

Q  =  5 x 4187 x (100 – 20)  =  1 674 800J  =  1.6748 MJ

Example 2

Calculate the amount of heat, in mega joules, that is necessary to raise 12 kg of steel from 30°C to 730°C.

Take the specific heat capacity steel to be 480 J/kg°C.

Q  =  mcΔt

Q  =  12 x 480 x (730 – 30)  =  4 032 000 J  =  4.032 MJ

Multiple Choice

Determine the quantity of heat energy required to raise the temperature of 5 kg of steel from 20°C to 800°C. Take the specific heat capacity (c) of steel as 480 J/kg°C.

Q = mcΔt

• 48,000J or 48kJ

• 1,900,000J or 1.92MJ

• 1,872,000J or 1.872MJ

• 80,000J or 80kJ

Multiple Choice

What quantity of heat, in megajoules (MJ), is necessary to raise the temperature of 6 kg of water from 20°C to 75°C?

Take the specific heat capacity of water to be 4200 J/kg°C.

• 1,890,000J or 1.89MJ

• 1,386,000J or 1.386MJ

• 1,890,000J or 1.89MJ

• 9000J ot 9kJ

Multiple Choice

What quantity of heat, in MJ, is necessary to raise the temperature of 12 kg of Copper from 20°C to 315°C?

Take the specific heat capacity of Copper to be 385 J/kg°C.

• 1,362,900J or 1.3629MJ

• 75,600J or 75.6kJ

• 92,400J or 92.4kJ

• 1,455,300J or 1.4553MJ

Specific latent heat

When a substance changes state (eg, when we melt metal we change it from a solid to a liquid) it uses heat energy for the transformation to take place.  To enable this to happen heat is added just to change the state and no change in temperature takes place.

When a change of state is from solid to liquid, this is called the; 

Specific latent heat of fusion

Example

1 kg of water at a temperature of 100°C requires 2257 kJ of heat energy to convert it into steam, ie the specific latent heat of vaporisation of water is 2257 kJ/kg

The symbol for latent heat is ‘h’.

This table gives typical values of latent heat, h, at atmospheric pressure, it takes extreme temperatures to vaporise metals.

As energy can neither be created nor destroyed, so likewise upon cooling the same amount of heat energy is given up by the substance during transformation.

So, if heat energy is being added to a substance and there is no rise in temperature, then the substance must be undergoing a change of state, i.e. solid to liquid or liquid to vapour.

The quantity of latent heat, Q required to change the state of a substance depends upon:

• The mass, m, of the substance—the larger the mass, the greater the heat energy required

• The specific latent heat, h, of the substance.

• Thus, the Quantity of latent heat energy  =  mass x latent heat

   or   

  Q  =  mh

  
  

  
  

Example 3

The specific latent heat required to melt ice is 335 kJ/kg.  Find the quantity of latent heat required to melt 3 kg of ice at 0°C.

where m = 3 kg h = 335 kJ/kg = 335 000 J/kg

Q  =  mh

Q  =  3 x 335 000

Q  =  1,005,000J = 1,005kJ =  1.005MJ

Multiple Choice

The specific latent heat required to melt aluminium is 9130 kJ/kg. Find the quantity of latent heat required to melt 4 kg of aluminium at 660°C

• 24,103,200J or 24.1032MJ

• 36,520J or 36.52kJ

• 36,520,000J or 36.52MJ

• 6025800J or 6.0258MJ

Multiple Choice

The specific latent heat required to melt copper is 3850 kJ/kg. Find the quantity of latent heat required to melt 1.5kg of copper at 1083°C

• 5,775J or 5.775kJ

• 4,169,550J or 4.16955MJ

• 1624.5J or 1,6245kJ

• 5,775,000J 5.775MJ