A researcher is heating a metal. He heats the metal so that the temperature of the metal rises at a constant rate. After 29 minutes of heating, the metal is 526˚C. After 41 minutes, the metal is 730˚C.
Choose the statement that best describes how the time and the temperature of the metal are related. Then, fill in the blank.
Statement 1: As time increases, the temperature of the metal decreases. The temperature of the metal decreases at a rate of ___˚C per minute.
Statement 2: As time increases, the temperature of the metal increases. The temperature of the metal increases at a rate of ___˚C per minute.
Statement 2: As time increases, the temperature of the metal increases. The temperature of the metal increases at a rate of 8˚C per minute.
Fill in the blank on Statement 1 as well, please.
Statement 1: As time increases, the temperature of the metal decreases. The temperature of the metal decreases at a rate of 8˚C per minute.
Now, what was the temperature of the metal when the researcher started heating it?
To calculate the initial temperature, we need to determine the rate of change in temperature per minute.
The change in temperature from 29 minutes to 41 minutes is (730˚C - 526˚C) = 204˚C.
The change in time is 41 minutes - 29 minutes = 12 minutes.
Therefore, the rate of change in temperature per minute is 204˚C / 12 minutes = 17˚C per minute.
Since we are assuming that the temperature was rising at a constant rate from the start, we can work backwards using the rate of change to find the initial temperature:
If after 29 minutes, the temperature was 526˚C, then:
526˚C = Initial temperature + (17˚C/minute * 29 minutes)
526˚C = Initial temperature + 493˚C
Initial temperature = 526˚C - 493˚C
Initial temperature = 33˚C
Therefore, the initial temperature of the metal when the researcher started heating it was 33˚C.