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THERMAL PHYSICS
Specific heat capacities

 copper 400Jkg-1K-1 iron 460Jkg-1K-1 water 4200Jkg-1K-1 ice 2100Jkg-1K-1

Specific latent heat of fusion of ice = 3.105Jkg-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 cross-section 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, T1 = 20°C.
The lower face of the plastic is maintained at a steady temperature, T4 = 150°C.
Calculate the temperatures of the surfaces of the metal, T2 and T3.
Assume that the heat lost through the sides of the metal (and plastic) is negligible.

7.   A rectangular piece of metal is 20.00c30.00cm, at 20°C.
The linear expansivity (linear expansion coefficient) for the metal, α =1×10-6°C-1.
Calculate:
a) the surface area, Ao 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 bi-metal strip?
ii)  What is a thermostat?
iii) Explain briefly how a bi-metal 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?

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