Mechanical Engineering Principles

HEAT ENERGY AND TRANSFER 213

Problem 3. Calculate the quantity of heat

required to raise the temperature of 5 kg of

water from 0°C to 100°C. Assume the

specific heat capacity of water is

4200 J/(kg°C).

Quantity of heat energy,

Q=mc(t 2 −t 1 )

=5kg×4200 J/(kg°C)×( 100 − 0 )°C

= 5 × 4200 × 100

=2100000 Jor2100 kJor 2 .1MJ

Problem 4. A block of cast iron having a

mass of 10 kg cools from a temperature of

150 °Cto50°C. How much energy is lost by

the cast iron? Assume the specific heat

capacity of iron is 500 J/(kg°C).

Quantity of heat energy,

Q=mc(t 2 −t 1 )

=10 kg×500 J/(kg°C)×( 50 − 150 )°C

= 10 × 500 ×(− 100 )

=−500000 Jor−500 kJor− 0 .5MJ

(Note that the minus sign indicates that heat is given
out or lost).

Problem 5. Some lead having a specific

heat capacity of 130 J/(kg°C) is heated from

27 °C to its melting point at 327°C. If the

quantity of heat required is 780 kJ, determine

the mass of the lead.

Quantity of heat, Q=mc(t 2 −t 1 ),hence,

780 × 103 J=m×130 J/(kg°C)

×( 327 − 27 )°C

i.e. 780000 =m× 130 × 300

from which, mass, m=

780000

130 × 300

kg=20 kg

Problem 6. 273 kJ of heat energy are

required to raise the temperature of 10 kg of

copper from 15°Cto85°C. Determine the

specific heat capacity of copper.

Quantity of heat, Q=mc(t 2 −t 1 ),hence:

273 × 103 J=10 kg×c×( 85 − 15 )°C

wherecis the specific heat capacity, i.e.

273000 = 10 ×c× 70

from which,specific heat capacity,

c=

273000

10 × 70

=390 J/(kg°C)

Problem 7. 5.7 MJ of heat energy are

supplied to 30 kg of aluminium that is

initially at a temperature of 20°C. If the

specific heat capacity of aluminium is

950 J/(kg°C), determine its final

temperature.

Quantity of heat, Q=mc(t 2 −t 1 ),hence,

5. 7 × 106 J=30 kg×950 J/(kg°C)

×(t 2 − 20 )°C

from which,(t 2 − 20 )=

5. 7 × 106

30 × 950

= 200

Hence thefinal temperature,

t 2 = 200 + 20 = 220 °C

Problem 8. A copper container of mass

500 g contains 1 litre of water at 293 K.

Calculate the quantity of heat required to

raise the temperature of the water and

container to boiling point assuming there are

no heat losses. Assume that the specific heat

capacity of copper is 390 J/(kg K), the

specific heat capacity of water is

4.2 kJ/(kg K) and 1 litre of water has a mass

of 1 kg.

Heat is required to raise the temperature of the

water, and also to raise the temperature of the copper

container.

For the water: m=1kg,t 1 =293 K,

t 2 =373 K (i.e. boiling point)

and c= 4 .2 kJ/(kg K)