The temperature
What is the initial temperature of the object?
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The temperature
What is the initial temperature of the object?
In a room with temperature 12°C, coffee is poured into a cup. The temperature of the coffee when it is poured into the cup is 92°C, and it is far too hot to drink.
The temperature,
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i.
ii.
A bottle of water, with temperature 5°C, is placed on a table in a room. The temperature of the room remains constant at 25°C. After
The temperature of the water can be modelled using the differential equation
where
After 8 minutes, the temperature of the water is 10°C.
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A refrigerator has a constant temperature of 3°C. A can of drink with temperature 30°C is placed in the refrigerator.
After being in the refrigerator for 15 minutes, the temperature of the can of drink is 28°C.
The change in the temperature of the can of drink can be modelled by
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a.
b.
A container of water is heated to boiling point (100°C) and then placed in a room that has a constant temperature of 20°C. After five minutes the temperature of the water is 80°C.
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a. | ||
(b)
A turkey is taken from the refrigerator. Its temperature is 5°C when it is placed in an oven preheated to 190°C.
Its temperature,
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At what time (to the nearest minute) will it be cooked? (3 marks)
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ii.
A salad, which is initially at a temperature of 25°C, is placed in a refrigerator that has a constant temperature of 3°C. The cooling rate of the salad is proportional to the difference between the temperature of the refrigerator and the temperature,
where
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ii.
Milk taken out of a refrigerator has a temperature of 2° C. It is placed in a room of constant temperature 23°C. After
where
How long does it take for the milk to reach a temperature of 10°C? (3 marks)
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To test some forensic science students, an object has been left in the park. At 10am the temperature of the object is measured to be 30°C. The temperature in the park is a constant 22°C. The object is moved immediately to a room where the temperature is a constant 5°C.
The temperature of the object in the room can be modelled by the equation
where
After one hour in the room the temperature of the object is 20°C.
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Find the time of day when the object had a temperature of 37°C. (3 marks)
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i.
ii.
A cup of coffee with an initial temperature of 80°C is placed in a room with a constant temperature of 22°C.
The temperature,
where
How long does it take for the temperature of the coffee to drop to 40°C? Give your answer to the nearest minute. (3 marks)
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