Mechanical Engineering Principles

HEAT ENERGY AND TRANSFER 217

(ii) Latent heat needed to change ice at 0°Cinto

water at 0°C is given by:

Q 2 =mLf= 0 .4kg×335 kJ/kg

=134 kJ

(iii) Heat energy needed to change the temperature
of water from 0°C (i.e. melting point) to
100 °C (i.e. boiling point) is given by:
Q 3 =mc(t 2 −t 1 )

= 0 .4kg× 4 .2 kJ/(kg°C)× 100 °C

=168 kJ

(iv) Latent heat needed to change water at 100°C
into steam at 100°C is given by:
Q 4 =mLv= 0 .4kg×2260 kJ/kg

=904 kJ

(v) Heat energy needed to change steam at 100°C

into steam at 120°C is given by:

Q 5 =mc(t 1 −t 2 )

= 0 .4kg× 2 .01 kJ/(kg°C)× 20 °C

= 16 .08 kJ

Total heat energy needed,

Q=Q 1 +Q 2 +Q 3 +Q 4 +Q 5

= 17. 12 + 134 + 168 + 904 + 16. 08

= 1239 .2kJ

Now try the following exercise

Exercise 99 Further problems on the

latent heats of fusion and

vaporisation

1. How much heat is needed to melt com-
   pletely 25 kg of ice at 0°C. Assume the
   specific latent heat of fusion of ice is
   335 kJ/kg. [8.375 MJ]


2. Determine the heat energy required to
   change 8 kg of water at 100°C to super-
   heated steam at 100°C. Assume the spe-
   cific latent heat of vaporisation of water
   is 2260 kJ/kg. [18.08 MJ]


3. Calculate the heat energy required to con-
   vert 10 kg of ice initially at− 30 °Ccom-
   pletely into water at 0°C. Assume the spe-
   cific heat capacity of ice is 2.1 kJ/(kg°C)
   and the specific latent heat of fusion of
   ice is 335 kJ/kg. [3.98 MJ]
   4. Determine the heat energy needed to con-
   vert completely 5 kg of water at 60°Cto
   steam at 100°C, given that the specific
   heat capacity of water is 4.2 kJ/(kg°C)
   and the specific latent heat of vaporisation
   of water is 2260 kJ/kg. [12.14 MJ]

19.6 A simple refrigerator

The boiling point of most liquids may be lowered

if the pressure is lowered. In a simple refrigerator

a working fluid, such as ammonia or freon, has the

pressure acting on it reduced. The resulting lowering

of the boiling point causes the liquid to vaporise. In

vaporising, the liquid takes in the necessary latent

heat from its surroundings, i.e. the freezer, which

thus becomes cooled. The vapour is immediately

removed by a pump to a condenser that is outside

of the cabinet, where it is compressed and changed

back into a liquid, giving out latent heat. The cycle

is repeated when the liquid is pumped back to the

freezer to be vaporised.

19.7 Conduction, convection and

radiation

Heat may be transferredfrom a hot body to a

cooler body by one or more of three methods,

these being: (a) byconduction, (b) byconvection,

or (c) byradiation.

Conduction

Conductionis the transfer of heat energy from one

part of a body to another (or from one body to

another) without the particles of the body moving.

Conduction is associated with solids. For exam-

ple, if one end of a metal bar is heated, the other end

will become hot by conduction. Metals and metal-

lic alloys are good conductors of heat, whereas air,

wood, plastic, cork, glass and gases are examples of

poor conductors (i.e. they are heat insulators).

Practical applications of conduction include:

(i) A domestic saucepan or dish conducts heat

from the source to the contents. Also, since

wood and plastic are poor conductors of heat

they are used for saucepan handles.