Newton's Law of Cooling: Consider a 98° C cup of coffee in a

[flakine]

Newton's Law of Cooling: Consider a 98° C cup of coffee in a

Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large.

Consider a 98 degree C cup of coffee in a 23 degree C room. Suppose it is known that the coffee cools at a rate of 1 degree C per minute when its temperature is 73 degree C. Use Euler's method with step size h=2 minutes to estimate the temperature of the coffee after 10 minutes.

Can someone help me to set this one up?

 

[skeeter]

let y = temperature at any time t

the rate of change of temperature of an object is directly proportional to the difference between the object's temperature and the temperature of its surroundings.

dy/dt = k(y - 23)

at y = 73, dy/dt = -1 deg/min

-1 = k(73 - 23)

k = -1/50

so ... dy/dt = (-1/50)(y - 23)

y(2) = y(0) + 2[(-1/50)(y(0) - 23)]

y(4) = y(2) + 2[(-1/50)(y(2) - 23)]

y(6) = y(4) + 2[(-1/50)(y(4) - 23)]

and so on til you get to y(10).