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A cold water has a temperature of 10 'c. It stands in the room of the temperature 30 'c. After 10 min the temperature of the water rises to 15 'c. The temperature y 'c,
rises at a rate that is proportional to the difference of 30-y.
a) Setup a diffrential equation that describes this situation.
b)What will be the temperature of water after 20 min.
c)How fast does the temperature rise when it is 20 'c.
I would be grateful if somebody could help me.
You could start with (a) the last sentence of the problem statement before it "The temperature 'y' in degrees centigrade,Quote:
Originally Posted by hejmh
rises at a rate that is proportional to the difference of '30-y' " is what you need to rewrite as a differential equation.
CB
I would use Newton's Law of Cooling on this one.
$\displaystyle \frac{dT}{dt} = k(30 - T)$
Seperate, integrate by parts.
Then solve for the constant using the known temperature $\displaystyle T = 10$ when $\displaystyle t = 0$
Solve for the constant of proportionality, $\displaystyle k$ by solving the equation when $\displaystyle T = 15$ when $\displaystyle t = 10$
