- #1

tracedinair

- 50

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## Homework Statement

a) An object at 200 degrees F is put in a room at 60 degrees F.The temperature of the room decreases at the constant rate of 1 degree every 10 minutes. The body cools to 120 degrees F in 30 minutes. How long will it take for the body to cool to 90 degrees F?

b) Show that the solution of the pertinent initial value problem which models the situation is:

T(t) = 60 + 140e^(kt) + [(e^(kt) - kt - 1)/(10k)]

c) Set-up an equation from which you can solve for k.

d) Set-up an equation from which the required cooling time can be found.

## Homework Equations

Newton's Law of Cooling: T'(t) = K(T(t) - T

_{0})

Note: T is in minutes

## The Attempt at a Solution

a) This is variable seperable

dT/dt = K(T(t) - T

_{0})

∫dT/(T(t) - T

_{0}) = ∫k dt + C

ln (T(t) - T

_{0}) = kt + C

(T(t) - T

_{0}) = ce^(kt)

T(t) = ce^(kt) + T

_{0}

At T(0) = 200, and T

_{0}= 60

200 = ce^(K*0) + 60

c = 140

T(t) = 140e^(kt) + 60

This is where I get stuck. I'm not really sure where to go next. I'm mainly confused by the fact that room temperature is decreasing as well.