Writing equation for integration regarding rate of change

In summary, the conversation discusses using Newton's law of cooling to determine the temperature of an object after being placed in water with a constant temperature. It is mentioned that the law only describes heat transfer from the object to the water, not the other way around. The idea of adding a minus sign to the derivative is suggested to account for heat transfer from the water to the object.
  • #1
Poppynz
6
0
Hi

An object with temperature 26 degrees Celsius is placed in water with constant temperature of 90 degrees Celsius. If the temperature of the object rises to 70 degrees Celsius in five minutes, what will be the temperature after 10 minutes?

I thought of using Newtons law of cooling d(temp)/d(t) = -k(constant of proportionality) (temp(object)-temp(surrounding medium)) but have read on the internet that it only describes transfer of heat from object to water not the other way around.

Any ideas would be appreciated
 
Physics news on Phys.org
  • #2
Well, if the object transfers some amount of heat to water, then you can say that the water transfers the same amount with opposite sign to the object,
And all you need to do is to add a minus sign in from of the derivative.
(I think so)
 

Related to Writing equation for integration regarding rate of change

What is integration regarding rate of change?

Integration regarding rate of change is a mathematical concept that involves finding the area under a curve, which represents the change in a quantity over time. It is used to analyze and understand how a variable changes over a given time period.

How is integration regarding rate of change related to calculus?

Integration regarding rate of change is a fundamental concept in calculus, which is the branch of mathematics that deals with change and motion. It is used to calculate the total change in a quantity over a given time interval, which is represented by the integral symbol (∫).

What are the steps for writing an equation for integration regarding rate of change?

The first step is to identify the function that represents the rate of change. This function is usually denoted by f(x) or dy/dx. Next, integrate the function using the integral symbol (∫). Finally, add the limits of integration to the equation to represent the time interval over which the change is being calculated.

What are the applications of integration regarding rate of change?

Integration regarding rate of change is used in various fields such as physics, economics, engineering, and biology to analyze and understand how quantities change over time. It is also used to calculate important values such as displacement, velocity, and acceleration.

What are some common mistakes to avoid when writing an equation for integration regarding rate of change?

Some common mistakes include forgetting to add the limits of integration, not using the correct notation for the function, and incorrectly identifying the function that represents the rate of change. It is also important to be careful when performing the integration and double check the final equation for any errors.

Similar threads

MHB How Does Newton's Law of Cooling Apply to a Roast Turkey?
    • Calculus
Replies
2
Views
862
A Practical use of an overall heat transfer coefficient?
    • Thermodynamics
Replies
14
Views
1K
MHB Differential Equations of Calculus Problems- Calc I course
    • Calculus
Replies
4
Views
3K
Thermodynamics - Temperature change of Argon
    • Introductory Physics Homework Help
Replies
19
Views
2K
What is the specific heat of the metal in this specific heat problem?
    • Introductory Physics Homework Help
Replies
3
Views
890
Flow Rate and Temperature Relationship in Air Change Calculations
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Convert Change in Temp from Celsius to Fahrenheit
    • Introductory Physics Homework Help
Replies
2
Views
2K
Amount of energy required to heat a kg of water?
    • Thermodynamics
Replies
6
Views
1K
MHB Sammy's question at Yahoo Answers regarding Newton's Law of Cooling
    • General Math
Replies
1
Views
2K
Can a Body of Water's Temperature Rise Linearly with Constant Heating?
    • Thermodynamics
Replies
19
Views
3K

Hot Threads

Recent Insights

Back
Top