Temperature Change of Apple Cobbler in Kitchen

In summary, the conversation discusses using Newton's law of cooling to determine the temperature of the kitchen where an apple cobbler is being held. The problem involves using the initial temperature of the cobbler, the temperature of the environment, and a material constant to solve for the room temperature. The individual seeking help had not considered this approach and found it helpful.
  • #1
Chrismb159
2
0
hi, i am having trouble with this problem...

An apple cobbler is taken out of the oven at 7:00PM one Saturday night. At that time it is piping hot at 100C. At 7:10PM its temperature is 80C, and at 7:20pm, it is 65C. What is the temperature of the kitchen in which the apple cobbler is being held?
 
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  • #2
What have you tried so far?
 
  • #3
To solve you may use Newton's law of cooling

[tex] \int_{T_{0}}^{T} \frac{dT}{T-T_{s}} = - \kappa \int_{t_{0}}^{t} d t^{\prime} [/tex]

where To is the initial temperature, Ts is the temperature of the environment (which is what we are after), k is a material constant, etc. Integrate both sides of this equation, and solve for T, and use the three boundary conditions to solve. You should get a reasonable answer for the room temperature. hope this helps, sincerely x
 
  • #4
thank you for that, we recently learned about that in physics but for some reason i couldn't put 2 and 2 together, i was going in a completely different direction.
 

FAQ: Temperature Change of Apple Cobbler in Kitchen

What is a differential equation problem?

A differential equation problem is a mathematical equation that involves an unknown function and its derivatives. These equations are used to model and describe a wide range of physical phenomena, and they are commonly used in physics, engineering, and other fields of science.

What is the difference between ordinary and partial differential equations?

An ordinary differential equation involves only one independent variable, while a partial differential equation involves multiple independent variables. This means that solutions to ordinary differential equations are functions of one variable, while solutions to partial differential equations are functions of multiple variables.

How are differential equations solved?

There is no single method for solving all types of differential equations. Some simpler differential equations can be solved analytically, while others require numerical methods or computer simulations. The specific method used depends on the type of differential equation and the available resources.

What are some real-world applications of differential equations?

Differential equations are used to model and analyze a wide range of physical phenomena, such as the spread of diseases, population growth, weather patterns, and chemical reactions. They are also used in engineering to design and optimize systems, such as electrical circuits and aircraft wings.

Are there any common techniques for solving differential equations?

Yes, there are several common techniques for solving differential equations, such as separation of variables, integrating factors, and series solutions. However, the specific technique used depends on the type of differential equation and its complexity.

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