Newtons Law of Cooling - Determine rate of cooling

In summary, the conversation discusses the use of calculus to determine the rate of fall of temperature for a particular engine that is switched off at 105°C and follows the equation T=105e-0.025t °C, where t is time in minutes. The concept of differentiation is mentioned as a necessary skill for solving these types of problems.
  • #1
Nokesy459
5
0
An engine switched off and left to cool naturally will obey Newtons law of cooling.
A particular engine is switched off at 105°C when the ambient temperature is 0°C. Its temperature falls according to the equation T=105e-0.025t °C. Where t=time in minutes.

c) use calculus to determine the rate of fall of temperature when t=80 minutes



I have no clue where to start! no matter how hard i look there's nothing to help..
 
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  • #2
The question asks for "the rate of fall of temperature" What does this mean in calculus?
 
  • #3
How do you mean?
 
  • #4
Have you had a course in calculus?
 
  • #5
No, This is self research and teaching
 
  • #6
I suspected that and was curious. I don't want to hijack BruceW's assistance...
 
  • #7
I don't mind others helping as well. The question asks for "rate of fall of temperature" Have you done similar problems, where you found the rate of change of some function?
 
  • #8
I have attempted, but the example i was using wasn't much help..
 
  • #9
Here's a simple example. Suppose temperature function is

T(t) = 2*e^(3t)

where t is time and T(t) is the temperature function in time.

The rate of temperature change is therefore

dT/dt = 6*e^(3t)

Can you take derivatives like the above?
 
  • #10
Lawrence has given a good example. There are a couple of simple rules for differentiating exponential functions. I'm guessing you've already done problems where you differentiated a polynomial function? Those are the kinds of functions that are learned first.

You need to learn about differentiation to do these kinds of problems. In some cases, there are simple rules for how to differentiate a function. And there are also things like the product rule and chain rule that can help us to differentiate more complicated functions. These are essential if you want to be able to master these kinds of problems!
 

1. What is Newton's Law of Cooling?

Newton's Law of Cooling is a mathematical equation that describes the rate at which an object cools down or loses heat when placed in a different temperature environment. It states that the rate of cooling is proportional to the temperature difference between the object and its surroundings.

2. How is the rate of cooling determined using Newton's Law of Cooling?

The rate of cooling can be determined by using the equation Q = -k(T - Ts), where Q is the amount of heat lost per unit time, k is the cooling constant, T is the temperature of the object, and Ts is the temperature of the surrounding environment.

3. What factors can affect the rate of cooling according to Newton's Law of Cooling?

The rate of cooling can be affected by several factors, including the temperature difference between the object and its surroundings, the surface area of the object, the type of material the object is made of, and the presence of any insulating materials.

4. Can Newton's Law of Cooling be applied to all objects?

Yes, Newton's Law of Cooling can be applied to all objects as long as they are in a uniform temperature environment and there are no external factors affecting the cooling process such as wind or radiation.

5. How is Newton's Law of Cooling used in real-world applications?

Newton's Law of Cooling is used in various real-world applications, such as determining the cooling rate of food and beverages, predicting the cooling of electronic devices, and studying the cooling of Earth's atmosphere. It is also used in industries such as meteorology, food preservation, and HVAC systems.

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