## Tuesday, 23 September 2014

### Thermal Physics Questions

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 = 3·3×105Jkg-1
Molar heat capacities of a diatomic ideal gas:
Cv = 12·5J(molK)-1 and Cp = 20·8J(molK)-1
Question 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 "final" temperature, after stirring, is 40°C. Calculate the specific heat capacity of the metal.
Question 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.
Question 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?
Question 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.
Question 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.
Question 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 lower face of the plastic is maintained at a steady temperature, T4 = 150°C. The top surface is maintained at a steady temperature, T1 = 20°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. Question 7
 A rectangular piece of metal is 20·00cm×30·00cm, at 20°C. The linear expansivity (linear expansion coefficient) for the metal is = 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 Compare this figure with the value of .
Question 8
 a) Considering question 9 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.
Question 9
 Two moles of an ideal gas are heated at a constant pressure of 105Pa. The temperature of the gas increases from 293K to 313K. Calculate a) the total amount of heat supplied b) the change in internal energy of the gas c) the work done by the gas during expansion d) the change in volume of the gas.
Question 10
 20mols of an ideal gas are in a cylinder of initial volume 0·5m3 at a temperature of 27°C. The gas is supplied with 10000J of heat at constant pressure. Calculate a) the final temperature of the gas b) the final volume of the gas c) the change in internal energy of the gas