Answer:
1) Temperature of the metal after 9 minutes = 269°C
2) [tex]Required\ temperature = 31\ min\ 37.5\ sec[/tex]
Step-by-step explanation:
Given:
Final temperature of the metal = 428°C
Temperature falls per minute for 3 minute = 23°C
Temperature falls per minute for next 15 minute = 15°C
Temperature falls per minute until room temperature = 8°C
We need to find the temperature after 9 minutes and what will be the time needed for the metal to reach a temperature of 25°C.
Solution:
First part:
As per given statement, the temperature of the metal falls at a rate of 23°C per minute for the first 3 minutes, so temperature falls in 3 minutes.
Temperature falls per minute = 23°C
Therefore,
[tex]Temperature\ falls\ for\ 3\ minute = 23\times 3[/tex]
Temperature falls for 3 minute = 69°C
After that temperature falls 15°C per minute for next 15 minute, so it is falls in
6 minutes.
Temperature falls per minute after 3 minutes = 15°C
Therefore,
[tex]Temperature\ falls\ for\ 6\ minutes\ after\ 3\ minutes = 15\times 6[/tex]
Temperature falls for 6 minutes after 3 minutes = 90°C
So temperature falls in 9 minutes = 90 + 69 = 159°C
So the temperature of the metal after 9 minutes = 428 - 159 = 269°C
Second part:
Temperature falls 23°C per minute for 3 minutes = 69°C
Temperature falls 15°C per minute for 15 minute = 225°C
So, leaving temperature after 18 minutes = Top temp - temp falls in 18 minutes.
Leaving temperature after 18 minutes = 428 - (69 + 225)
Leaving temperature after 18 minutes = 428 - (69 + 225)
Leaving temperature after 18 minutes = 134°C
Temperature falls 8°C per minute until it reaches room temperature of 25°C = 134 - 25 = 109°C
So the rate of the falling temperature = [tex]\frac{109}{8}= 13\frac{5}{8}=13\ min\ 37.5\ sec[/tex]
[tex]Required\ temperature = 31\ min\ 37.5\ sec[/tex]
Therefore, the required temperature of the metal to reach 25°C is equal to 31 min 37.5 sec.
