

Specific heat capacities 



copper 
400Jkg^{1}K^{1}


iron 
460Jkg^{1}K^{1}


water 
4200Jkg^{1}K^{1}


ice 
2100Jkg^{1}K^{1}







Specific latent heat of fusion of ice = 3.3×10^{5}Jkg^{1} 



1. 

A piece of metal of mass 0.2kg
is heated to a temperature of 200°C. 


It is then put into 0.2kg of
water at 20°C in a container of negligible heat capacity. 


The maximum temperature of the water, after stirring, is 40°C. 


Calculate the specific heat capacity of the metal. 



2. 

A piece of ice at 20°C is put into a copper calorimeter of mass
0.2kg which contains 0.15kg
of water at 20°C. 


The water is stirred until all the ice has melted. 


At this time the temperature of the water (and calorimeter) is
15°C. 


Calculate the mass of the piece of ice. 



3. 

A refrigerator is capable of removing 50J
of heat per second from a container of water. 


How long will it take to change 2kg
of water at 10°C into ice at 5°C? 


Assume that the rate of removal of heat remains constant and
that the container has negligible heat capacity. 


Are these assumptions likely to be valid in practice? 



4. 

A piece of metal of mass 100g,
has a temperature of 100°C. 


It is put into 100g of water at
20°C in a container of negligible heat capacity. 


After stirring, the maximum temperature of the mixture (metal
and water) is 27.5°C. 


Calculate the specific heat capacity of the metal. 



5. 

How long will it take to change the temperature of 200kg
of water from 15°C to 40°C, using a heater of power
3kW. 


Assume that all the thermal energy remains in the water. 



6. 

The diagram below show a crosssection view of a sheet of metal
(of thermal conductivity, k) covered on each side by a layer of
plastic of thermal conductivity k/1000. 











The top surface is maintained at a steady temperature, T_{1}
= 20°C. 


The lower face of the plastic is maintained at a steady
temperature, T_{4} = 150°C. 


Calculate the temperatures of the surfaces of the metal, T_{2}
and T_{3}. 


Assume that the heat lost through the sides of the metal (and
plastic) is negligible. 



7. 

A rectangular piece of metal is 20.00cm×30.00cm,
at 20°C. 


The linear expansivity (linear expansion coefficient) for the
metal, α
=1×10^{6}°C^{1}. 


Calculate: 

a) 
the surface area, A_{o} of the piece of metal at 20°C
(yes I know its difficult, but try…) 

b) 
the lengths of the sides of the piece of metal at 80°C 

c) 
the surface area, A, of the piece of metal at 80°C 

d) 
the value of the quantity 





(which is the surface area expansion coefficient for
the metal) where ΔA is change of area
and ΔT is change of temperature 


Compare this figure with the value of α 



8. 
a) 
Considering question 7 part d), define, in words, the area
expansion coefficient of a substance and state how it is
related to the linear expansion coefficient. 

b) 
Suggest a definition of the volume expansion coefficient
of a substance and predict how it might be related to the
linear expansion coefficient. 



9. 

Metals expand when they are heated and contract when they are
cooled. 

a) 
Describe briefly one problem caused by the expansion of metals. 

b) 
i) What is a bimetal strip? 


ii) What is a thermostat? 


iii) Explain briefly how a bimetal strip can be used to make an
electrical thermostat. 



10. 
a) 
In what way is the expansion and contraction of water unusual? 

b) 
State the temperature at which water has its maximum density. 

c) 
Describe one problem caused by the unusual expansion of
water and one advantage it brings 



11. 

The specific heat capacity of water is very high. 


What effect does this have on the weather conditions experienced
by people living on islands? 