Mechanical Engineering Principles

214 MECHANICAL ENGINEERING PRINCIPLES

Quantity of heat required for the water is given by:

QW=mc(t 2 −t 1 )

=(1kg)

(

4. 2

kg

kg K

)

( 373 − 293 )K

= 4. 2 ×80 kJ

i.e. QW=336 kJ

For the copper container:

m=500 g= 0 .5kg,t 1 =293 K,

t 2 =373 K and

c=390 J/(kg K)= 0 .39 kJ/(kg K)

Quantity of heat required for the copper container is
given by:

QC=mc(t 2 −t 1 )

=( 0 .5kg)( 0 .39 kJ/(kg K)(80 K)

i.e. QC= 15 .6kJ

Total quantity of heat required,

Q=QW+QC= 336 + 15. 6 = 351 .6kJ

Now try the following exercise

Exercise 97 Further problems on specific

heat capacity

1. Determine the quantity of heat energy (in
   megajoules) required to raise the tem-
   perature of 10 kg of water from 0°Cto
   50 °C. Assume the specific heat capacity
   of water is 4200 J/(kg°C). [2.1 MJ]


2. Some copper, having a mass of 20 kg,
   cools from a temperature of 120°Cto
   70 °C. If the specific heat capacity of
   copper is 390 J/(kg°C), how much heat
   energy is lost by the copper? [390 kJ]


3. A block of aluminium having a specific
   heat capacity of 950 J/(kg°C) is heated
   from 60°C to its melting point at 660°C.
   If the quantity of heat required is 2.85 MJ,
   determine the mass of the aluminium
   block. [5 kg]


4. 20.8 kJ of heat energy is required to raise
   the temperature of 2 kg of lead from
   16 °Cto96°C. Determine the specific
   heat capacity of lead. [130 J/kg°C]
   5. 250 kJ of heat energy is supplied to 10 kg
   of iron which is initially at a temperature
   of 15°C. If the specific heat capacity of
   iron is 500 J/(kg°C) determine its final
   temperature. [65°C]

19.4 Change of state

A material may exist in any one of three

states — solid, liquid or gas. If heat is supplied at a

constant rate to some ice initially at, say,− 30 °C, its

temperature rises as shown in Figure 19.1. Initially

the temperature increases from− 30 °Cto0°Cas

shown by the lineAB. It then remains constant at

0 °C for the timeBCrequired for the ice to melt

into water.

120

100

80

60

Temperature /

°C

40

20

0

− 30

A

BC

DE

F

Time

Figure 19.1

When melting commences the energy gained by

continual heating is offset by the energy required

for the change of state and the temperature remains

constant even though heating is continued. When

the ice is completely melted to water, continual

heating raises the temperature to 100°C, as shown

byCDin Figure 19.1. The water then begins to

boil and the temperature again remains constant

at 100°C, shown asDE, until all the water has

vaporised.

Continual heating raises the temperature of the

steam as shown byEF in the region where the

steam is termed superheated.

Changes of state from solid to liquid or liquid to

gas occur without change of temperature and such