A cake is removed from an oven and its temperature is 350°F. Assume room temperature is 70°F. Five minutes later, the temperature of the cake is 250°F. How long will it take for the cake to cool to 90°F? The rate of change of the temperature of the cake is proportional to the difference between the temperature of the cake and the temperature of the room, so dT(1) 2 =k (T(t)-T„) where T(t) represents the temperature of an object at time t. dt T_ is the temperature of the room. dT(t) 2= k (T(1)-T„) for T(t). dt a) First, solve the differential equation The result should be T(t)=T,,+Ce" .
A cake is removed from an oven and its temperature is 350°F. Assume room temperature is 70°F. Five minutes later, the temperature of the cake is 250°F. How long will it take for the cake to cool to 90°F? The rate of change of the temperature of the cake is proportional to the difference between the temperature of the cake and the temperature of the room, so dT(1) 2 =k (T(t)-T„) where T(t) represents the temperature of an object at time t. dt T_ is the temperature of the room. dT(t) 2= k (T(1)-T„) for T(t). dt a) First, solve the differential equation The result should be T(t)=T,,+Ce" .
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:b) Fill in the blanks in this table using the facts stated in the problem, Use the first two
rows to determine the values of C and k in T(t)=T +Ce.
半
Also, T_ =
5
So the formula is T(1)=.
c) Now find the time when the temperature of the cake is 90°F.
Complete the table.
T
5
90°F
Transcribed Image Text:A cake is removed from an oven and its temperature is 350°F. Assume room
temperature is 70°F. Five minutes later, the temperature of the cake is 250°F.
How long will it take for the cake to cool to 90°F?
The rate of change of the temperature of the cake is proportional to the difference
between the temperature of the cake and the temperature of the room, so
ar -k (T(t)-T) where T(t) represents the temperature of an object at time t.
dt
T is the temperature of the room.
dT(t).
di (1) – k (T(t)–T„) for T(t).
dt
a) First, solve the differential equation
The result should be T(t) =T +Ce.
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