Mixing hot and cold water

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Key Learning Points

1. Heat
2. Specific Heat Capacity
3. Mixing

Video sample

	Mixing hot and cold water.
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Suppose you want to drink a glass of warm water in an afternoon. But you only have some hot water in the kettle and some cold water in the refrigerator. So you mix them together to prepare a glass of warm water. If the temperatu res of the hot and cold water are known, what proportion of hot water to cold water should be used to prepare a glass of warm water of a given temperature? Can you perform an experiment to verify this result?

Datalogger, temperature sensors, polystyrene cups (about 200 ml), electronic balance, plasticine, measuring cylinders (250 ml), vacuum flask and stirrer.

We will now perform this experiment of mixing. Suppose we want to prepare a cup of water of temperature 40 by mixing hot and cold water.

1. Heat up some water to about 75 and pour it into a vacuum flask.
2. Put some water in the refrigerator until its temperature becomes about 5 .
3. Use a piece of plasticine to fix the temperature sensor to the polystyrene cup. Make sure that the bottom of the sensor is not in contact with the container.
4. Measure the mass of the empty polystyrene cup and temperature sensor using the electronic balance.
5. Measure about 100 ml of cold water (about 5 ) with a measuring cylinder and pour it into the polystyrene cup. Measure the water temperature. After measuring the temperature, pour the cold wate r into another polystyrene cup.
6. Measure about 50 ml of hot water (about 75 ) with a measuring cylinder and pour it into the polystyrene cup and measure the water temperature.
7. Measure the mass of the system and find out the mass of hot water.
8. Pour the cold water slowly into the hot water. Keep on pouring and stirring until the temperature of the mixture becomes 40 .
9. Note the final reading of the electronic balance. Find out the mass of cold water used. Thus find out the proportion of hot water to cold water.
10. Suppose the proportion of hot water to cold water is : 1. Calculate the value of using the temperatures of hot and cold water you used in the exp eriment. Does it agree with the value found in step 10?

Given: Specific heat capacity of water = 4200 .

1. How do you calculate the ratio of hot water to cold water ?
2. Does the calculated ratio agree with that found in the experiment? Why?
3. Why do we have to record the initial temperatures of the hot and cold water just before mixing, but not at the moment of preparing them?
4. Why do we use polystyrene cups instead of glass cups? In daily life, we often use glass cups to hold drinking water. How do you expect the result of this experiment to change if glass cups are used? Explain.
5. What is the advantage of using datalogger and temperature sensor instead of liquid-in-glass thermometer in this experiment?
6. What is possible experiment error of temperature measurement?
7. Does the result of this experiment depend on the value of specific capacity of water? Would we get the same ratio if hot oil and cold oil are used instead of water?