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 Heat capacity, C The amount of heat required to change its temperature by one degree.

Specific Heat Capacity, c The amount of heat that must be supplied to increase the temperature by 1 °C for a mass of 1 kg othe substance

Specific heat capacity, c = Q SI unit: = J kg-1

°C-1

mθ 

Q = heat absorbed / released, unit Jm = mass of the substance, unit kgθ = temperature difference , unit °C

Quantity of heat absorbed orlost by a substance Q = mcθ

What does specific heat ofaluminium

900 J kg-1

°C-1

mean?

900 J of heat needs to be supplied to 1 kg of aluminium to produce a 1 °C temperature increase

What does specific heat of

water 4 200 J kg-1

°C-1

mean?4 200 J of heat needs to be supplied to 1 kg of water to produce a 1 °C temperature increase.

The physical meaning of

specific heat capacity, c

When two objects of equal mass are heated at equal rates, the temperature of the object with the

smaller specific heat capacity will rise faster.When two objects of equal mass are left to cool down, the temperature of the object with smallerheat capacity will drop faster .

Substance with a small valueof specific heat capacity

  heats up and cools at a faster rate.For example, metal like iron, steel, copper and aluminium is used as pots and pans because theycan be quickly heated up when there is only small heat absorption.

  sensitive to temperature changes A thermometer has low specific heat capacities so it enables heat to be easily absorbed andreleased even when small quantities of heat are involved.

Substance with a high valueof specific heat capacity

  Heats up and cools at slower rate. Require more heat to raise its temperature by aspecific amount.

  Poor conductor of heat – handle of pot

  can absorb a great amount of heat without a high increase in temperature.

  For example, water acts a heat reservoir as it can absorb a great amount of heat before itboils. Water is used as a cooling agent in a car radiator. 

Solve Problem

Example 1Calculate the total heat that is observed by a copper block ofmass 500 g and which has been heated from 31 °C to 80°C.

(specific heat capacity of copper = 390 JKg-1

°C-1

)SOLUTION:

Q = mcθ 

= 0.5 kg x 390 JKg-1

°C-1

 x (80-31)= 9555J 

Example 2When an electric heater is supplied with an electric power of 2kW to heat 4 kg of water for 1 minute, calculate the increase intemperature of the water. [specific heat capacity of water = 4 200

JKg-1

°C-1

) Assume there is no heat loss to the surroundings

Example 3

 A lead bullet moves horizontally with a velocity of 130 ms-1

andembedded into a cement wall after collision. If the specific heat

capacity of lead = 130 JKg-1

°C-1

and all heat produces isabsorbed by the bullet, what is the increase in temperature of thebullet?

Example 4

 An aluminium block of mass 1 kg is heated by an electric heaterfor 3 minutes and a temperature rise of 15 °C is recorded. If theelectric heater is connected to a voltmeter which gives a readingof 30 V and an ammeter which gives a reading of 2.5 A, calculatethe specific heat capacity of the aluminium

Example 5300 g of water at temperature 40 °C is mixed with 900 g of waterat temperature 80 °C. If there is no heat loss to the surroundings,what is the final temperature when thermal equilibrium isachieved by the mixture of water?

Example 6320g of hot water at 80oC is poured into an aluminium can ofmass 35g and temperature of 20

oC. Calculate the final

temperature.

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Application of Specific Heat Capacity

Cooking pot a) Copper base • Low specific heat capacity. The pot becomes hot very quickly. Thisenables quick cooking of the food in the pot.

• High density. The heavier base ensures that the pot is stable and willnot topple over easily.

(b) Wooden Handle• Large specific heat capacity. The handle will not become too hot whenheat is absorbed.• Poor conductor of heat.(c) Alumni body

• Relatively low specific heat capacity. The pot becomes hot quickly.• Low density so it will be lighter• Does not react with the food in the pot

Sea Breeze• Land has a smaller specific heat capacity than sea. Fasterincrease intemperature, ie land is warmer than the sea

• Air above the land is heated up and rises.• Cooler air from the sea moves from towards the land assea breeze. 

Land Breeze

• At night, heat is lost from the land and sea.• Sea has a larger specific heat capacity so sea is warmerthan land.

• Warmer air above the sea rises• Cooler air from the land moves towards the sea as land

breeze.

The cooling system of a car engine Water is used as a coolant in car engines because

has a high Specific heat capacity Easily obtained and cheap,

Does not chemically react with the materials in theengine

  A water pump circulates the water.

  Heat produced by the engine is absorbed by the waterthat flows along the space in engine walls.

  The hot water flows to the radiator where heat is lost tothe cooler air that flows through the cooling fans. 

Characteristics of the liquid used in radiator

  High specific heat capacity so can store more heat

  High boiling point so turn a gas slowly 

 A boy drinking hot soup with a spoon. If he

accidentally spills a spoonful of soup onto his hand,he would experience only a slight pain. However, ifhe spills the whole contents of the bowl of souponto himself, he would suffer serious injuries.

• The mass of the spoonful soup is smaller than the mass of the

whole bowl of soup although both are at the same temperatureand have same specific heat capacity.

• Q = mcθ• The mass is directly proportional to the quantity of heat.• The soup in the bowl contains more heat

Characteristics of container to store hot food and can be moved easily.

  High specific heat so it is not easily heated

  High melting point so does not melt easily when hot food is put into it.

  Low density so lighter

  Low thermal conductivity so heat is not lost easily

  Vacuum space to prevent heat lost.

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TUTORIAL 4.2

1. Diagram 3.1 shows a metal block P of mass 300 g at initialtemperature 100

oC is immersed into the water at room

temperature. Diagram 3.2 shows the graph of temperatureagainst time of block P until it achieve thermal equilibrium

(a) What is meant by thermal equilibrium?

(b) What is the temperature of block P when it is in thermalequilibrium?

(c) Explain how block P achieve thermal equilibrium.

(d) Calculate the amount of heat lost by block P when itsachieved thermal equilibrium.[Specific heat capacity of block P = 900 J kg

-1 oC

-1 ]

2. Diagram 7.1 shows a cooling pad used to lower thetemperature of a person having fever. The pad consists of a geland is cooled in a refrigerator before it is placed on the foreheadof the person to remove the heat.

(a) (i) What is meant by heat?

(ii) Explain how the heat is removed from the forehead of theperson

(b) The mass of the gel in the pad is 30 g and its’ specific heat capacity is 4.3 J g-1 ˚C-1. The initial temperature of the pad is15 ˚C and the final temperature is36 ˚C. Calculate the amount ofheat removed by the pad.

(c) It is suggested that the cooling pad should be modified so thait can remove more heat. Give two suggestion and the reasonsfor doing so.

Suggestion 1:Reason:

Suggestion 2:Reason:

2. A block of copper with mass of 200 g is heated to 100 ˚C inboiling water. The hot copper is then quickly transferred to

a beaker containing 700 g of water at 30˚C as shown in Diagram3. After 2 minutes the thermal equilibrium is achieved and thefinal temperature is 80 ˚C.

(a) (i) Determine the difference in temperature between theboiling water and the water in the beaker as shown in Diagram 3.

(ii) What is the net flow of heat during the thermal equilibrium?

(b) On Diagram below using directed lines, show the direction ofheat transfer between the water and the block copper

c) The specific heat capacity of copper is 400 J kg-1

 oC

-1

Calculate heat energy released by the copper[2 marks

(d) The specific heat capacity of water is 4200 J kg 1 º C 1 .What is the raise of temperature of 1 kg of water when supplywith 12600 joule of heat energy

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