# defferiantial equation

• Jun 6th 2008, 11:47 PM
khuezy
defferiantial equation
When a cake is removed from an oven, the temperature of the cake is 210F. The cake is left to cool at room temperature (70F.), and after 30 minutes, the temperature of the cake is 140F
According to Newton's law of cooling, the rate of change of temperature of a body is proportional
to the temperature difference between the body and the environment. Set up and solve a differential
equation to determine when the temperature of the cake will be 100F.

How would you set up this problem?
• Jun 6th 2008, 11:56 PM
mr fantastic
Quote:

Originally Posted by khuezy
When a cake is removed from an oven, the temperature of the cake is 210F. The cake is left to cool at room temperature (70F.), and after 30 minutes, the temperature of the cake is 140F
According to Newton's law of cooling, the rate of change of temperature of a body is proportional
to the temperature difference between the body and the environment. Set up and solve a differential
equation to determine when the temperature of the cake will be 100F.

How would you set up this problem?

The DE is $\frac{dT}{dt} = k (T - 70)$

subject to the boundary conditions T(0) = 210 and T(30) = 140.

The boundary conditions are used to find the value of arbitrary constant of integration and the proportionality constant k.

Solve the DE. Use the solution to find the value of t when T = 100.

I suggest you carefully study examples from your class notes and/or textbook, as well as using the search string Newton Law Cooling in a famous search engine ....
• Jun 7th 2008, 12:02 AM
Jhevon
Quote:

Originally Posted by mr fantastic
The DE is $\frac{dT}{dt} = k (T - 70)$

subject to the boundary conditions T(0) = 210 and T(30) = 140.

The boundary conditions are used to find the value of arbitrary constant of integration and the proportionality constant k.

Solve the DE. Use the solution to find the value of t when T = 100.

I suggest you carefully study examples from your class notes and/or textbook, as well as using the search string Newton Law Cooling in a famous search engine ....

Here's an example. See the first part of post #2

More examples: posts # 2 and 8