RGS Prelims 1997 P2 Q10
(a) The figure below shows an experiment on heat transfer.
(i) State the means of heat transfer from the heater to thermometers X and Y.
(ii) Which thermometer will have a higher temperature change after a certain time?
(iii) If the heater is placed between thermometers X and Y, determine which one will register a higher change. Give reasons.
(b) A 3 kW immersion heater is used to keep the water in a domestic hot water tank at a steady temperature. The electrical supply to the immersion heater is switched off when the average water temperature is 60 °C. Assuming that the rate of heat loss is constant at 1.8 kW and no water is run off, and that the total heat capacity of the tank and the water it contains is 5.2 * 105 J K-1, calculate the average temperature 40 minutes later.
(c) Liquid air boils at a very low temperature at normal atmospheric pressure. Explain why liquid air contained in an open vacuum flask in a laboratory boils steadily and continuously. Why does liquid air boil much more rapidly when contained in an ordinary glass beaker?
(d) A 20 g lump of iron is placed in liquid air for several minutes. It is then removed and quickly placed in water at 0 °C. A 5.2 g layer of ice forms over the iron. Determine the temperature of the liquid air. (The specific heat capacity of iron is 440 J kg-1 °C-1 and the latent heat of fusion of ice is 3.34 * 105 J kg-1.)
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Answer:
(a)
(i) Conduction (Not convection because heater is on top, and hot water rises)
(ii) Thermometer X (nearer to heater)
(iii) Thermometer X. This is because hot water rises and cold water sinks. The water above the heater (where thermometer X is) will get heated up faster.
(b) Using Q = CΔӨ,
1.8 * 1000 * (40 * 60) = 5.2 * 105 * ΔӨ
ΔӨ = (4.32 * 106) / (5.2 * 105)
ΔӨ = 8.3 °C
Hence, average temperature = 60 °C - 8.3 °C = 51.7 °C
(c) Liquid air contained in an open vacuum flask in a laboratory boils steadily and continuously because the room temperature is always higher than the boiling point of liquid air; heat energy is being constantly supplied from the surroundings to the liquid air to boil it continuously.
Liquid air boils much more rapidly when contained in an ordinary glass beaker because in an ordinary glass beaker, heat energy is also supplied through conduction via the sides of the beaker. Heat transfer to liquid air in a vacuum flask is limited to conduction via the hole/entrance of the vacuum flask. Thus, we can see that heat energy is being supplied at a higher rate for the glass beaker as compared to the vacuum flask (more channels/surface area for heat transfer). This explains why liquid air boils much more rapidly when contained in an ordinary glass beaker.
(d) Let the temperature of liquid air be T
Heat gained by Iron = Latent heat loss to change from water at 0 °C to ice at 0 °C.
mciron ΔӨ = mlfusion
(0.020)(440)(0 - T) = (0.0052)(3.34 * 105)
-8.8T = 1736.8
T = -197 °C
Note: A quick way to check... Boiling point of liquid nitrogen is around -196 °C, so since air is mainly nitrogen, -197 °C sounds very logical.
