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akeemsimpson15p2034o
28.06.2020 •
Mathematics
Two large containers A and B of the same size are lled with different uids. The uids in containers A and B are maintained at 0° C and 100° C, respectively. A small metal bar, whose initial temperature is 100° C, is lowered into container A. After 1 minute the temperature of the bar is 90° C. After 2 minutes the bar is removed and instantly transferred to the other container. After 1 minute in container B the temperature of the bar rises 10°. How long, measured from the start of the entire process, will it take the bar to reach 99.9° C?
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Ответ:
t = 9.05 min
Step-by-step explanation: The rate of temperature over time is given by:
where:
K is the constant of transference of heat
ln (T -
) = kt + c
In container A, the temperature is at 0°C, so
For the bar, when t = 0 min, T = 100°C:
100 =![Ce^{k.0}](/tpl/images/0696/4738/bdcc8.png)
C = 100
After 1 minute, the temperature of the bar is 90°C, so:
k = ln(0.9)
k = - 0.105
After 2 minutes, the temperature will be:
T = 81.06°C
For container B, the temperature is 100°C, so:
The initial temperature of the bar when entering the container B is T = 81.06°C, then:
C = - 18.94
After 1 minute, the temperature rises 10°C:
91 =![- 18.94e^{k.1} + 100](/tpl/images/0696/4738/911ba.png)
k = ln(0.475)
k = - 0.744
When T = 99.9°C:
t =![\frac{ln(0.0053)}{-0.744}](/tpl/images/0696/4738/b87c5.png)
t = 7.05 min
The entire process will take:
t = 2 + 7.05
t = 9.05 min
Ответ:
answer:
step-by-step explanation: