3.1.1 Calculation of heat quantities

 

a)            Sensible Heat

When a substance change temperature the amount of sensible heat absorbed or released is given by the formula:

Q = mcѲ

Wheres:

Ǫ = quantity of sensible heat (J)

m = mass of substance (kg)

c = specific heat capacity of the substance (J/kg°C)

Ѳ = Ѳ2 – Ѳ1 = temperature change (°C)

Example 3.3

A storage heater contains concrete blocks with total dimensions of 800mm by 500mm by 220mm. The concrete has a density of 2400kg/m³ and a specific heat capacity of 3300J/kg °C. ignoring heat losses, calculate the quantity of heat required to raise the temperature of the blocks from 15°C to 35°C

Volume             =          0.8 x 0.5 x 0.22

=          0.088m³

Density (p)        =             mass (m)_

                                      Volume (v)

Mass (m)          =          density (p) x volume (v)

m                     =          2400 x 0.088

=          211.2kg

Using formula:

Ǫ          =          mcѲ

=          211.2 x 3300 x (35-13)

=          13 939 200J

Q          =          13.94MJ

b)            Latent Heat

During a change of state in a substance the amount of latent heat absorbed or released is given by the formula:

Q = ml

Wheres:

Q = quantity of latent heat (J)

m = mass of substance

l = specific latent heat for that change of state (J/kg)

Specific latent heat (l) is a measure of the latent heat absorbed or released from a particular material for a given change of state. Unit : J/kg

Specific enthalpy change and some common values are:

Specific latent heat of ice = 335 000J/kg   ≈ 335kJ/kg

Specific latent heat of steam = 2260 000J/kg    ≈ 2260 kJ/kg

  

Example 3.4

Calculate the total heat energy required to convert 2kg of ice at 0°C completely to steam at 100°C. The specific heat capacity of water is 4190J/kg°C. The specific latent heats are 335kJ/kg for ice and 2260kJ/kg for steam.

 

Answer 3.4

i.      Changing ice at 0°C to water at 0°C requires latent heat.

Using Q = ml

Q1 = 2 x 335 000 = 670 000J

Q1 = 670kJ

ii.     Changing water at 0°C to water at 100°C required sensible heat.

Using Ǫ = mcѲ

Q2  = 2 x 4190 x 100 = 838 000J

Q2  = 838kJ

iii.    Changing water at 100°C to steam at 100°C required latent heat

Using Q = ml

Q3  = 2 x 2260 000 = 4520 000J

Q3  = 4520kJ

Total heat required             = Q1 + Q2 + Q3

                                                = 670 + 838 + 4520

                                                = 6028kJ