To calculate the temperature changes ([tex]\(\Delta T\)[/tex]) at each time interval provided in the table, follow these steps:
1. Initial Temperature:
- The initial temperature is given as [tex]\(15^\circ C\)[/tex]. Since this is our reference point, the temperature change at this point is [tex]\(0^\circ C\)[/tex].
2. Temperature after 5 minutes:
- Temperature at this time is [tex]\(17^\circ C\)[/tex].
- To find the temperature change ([tex]\(\Delta T\)[/tex]), subtract the initial temperature from the temperature at 5 minutes:
[tex]\[
\Delta T = 17^\circ C - 15^\circ C = 2^\circ C
\][/tex]
3. Temperature after 10 minutes:
- Temperature at this time is [tex]\(20^\circ C\)[/tex].
- To find the temperature change ([tex]\(\Delta T\)[/tex]), subtract the initial temperature from the temperature at 10 minutes:
[tex]\[
\Delta T = 20^\circ C - 15^\circ C = 5^\circ C
\][/tex]
4. Temperature after 20 minutes:
- Temperature at this time is [tex]\(23^\circ C\)[/tex].
- To find the temperature change ([tex]\(\Delta T\)[/tex]), subtract the initial temperature from the temperature at 20 minutes:
[tex]\[
\Delta T = 23^\circ C - 15^\circ C = 8^\circ C
\][/tex]
Using these calculations, we can fill in the table as follows:
[tex]\[
\begin{array}{|c|l|l|}
\hline
\text{Time} & \text{Temperature, } {}^{\circ}C & \text{Temperature change, } {}^{\circ}C (\Delta T) \\
\hline
\text{Initial} & 15^\circ C & 0^\circ C \\
\hline
5 \text{ minutes} & 17^\circ C & 2^\circ C \\
\hline
10 \text{ minutes} & 20^\circ C & 5^\circ C \\
\hline
20 \text{ minutes} & 23^\circ C & 8^\circ C \\
\hline
\end{array}
\][/tex]
These results represent the changes in temperature at each measured interval.
