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A researcher is heating a metal. He heats the metal so that the temperature of the metal rises at a constant rate. After 30 minutes of heating, the metal is 446°C. After 50 minutes, the metal is 726°C.(a)Choose the statement that best describes how the time and the temperature of the metal are related. Then fill in the blank.As time increases, the temperature of the metal decreases.Thetemperatureofthemetaldecreasesatarateof°Cperminute. As time increases, the temperature of the metal increases.Thetemperatureofthemetalincreasesatarateof°Cperminute. (b)What was the temperature of the metal when the researcher started heating it?°C

Question

A researcher is heating a metal. He heats the metal so that the temperature of the metal rises at a constant rate. After 30 minutes of heating, the metal is 446°C. After 50 minutes, the metal is 726°C.(a)Choose the statement that best describes how the time and the temperature of the metal are related. Then fill in the blank.As time increases, the temperature of the metal decreases.Thetemperatureofthemetaldecreasesatarateof°Cperminute. As time increases, the temperature of the metal increases.Thetemperatureofthemetalincreasesatarateof°Cperminute. (b)What was the temperature of the metal when the researcher started heating it?°C

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Solution

(a) As time increases, the temperature of the metal increases. The temperature of the metal increases at a rate of (726°C - 446°C) / (50 min - 30 min) = 14°C per minute.

(b) To find the initial temperature of the metal, we can use the rate we found and the information given. We know that after 30 minutes, the metal was 446°C. So, if the temperature was increasing at a rate of 14°C per minute, then the temperature of the metal when the researcher started heating it was 446°C - (30 min * 14°C/min) = 446°C - 420°C = 26°C.

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