Solving Newtons Cooling Law: LnT = -kt +LnC

[xlgurulx]

Newtons cooling law?

Homework Statement

uh for my lab report the problem is i have to solve for the constnat and the lnC? look below

Homework Equations

teacher said something about LnT =Lne^-kt +LnC
transposes into ==> LnT = -kt +LnC
uh and i have the temperatures to do this.. but i don't know exactly what I am trying to do

The Attempt at a Solution

seen as i don't know how to do it and I am only in precalc i don't really get what I am trying to do... as well can someone explain what this formula means?

 

[LowlyPion]

Homework Statement

uh for my lab report the problem is i have to solve for the constnat and the lnC? look below

Homework Equations

teacher said something about LnT =Lne^-kt +LnC
transposes into ==> LnT = -kt +LnC
uh and i have the temperatures to do this.. but i don't know exactly what I am trying to do

The Attempt at a Solution

seen as i don't know how to do it and I am only in precalc i don't really get what I am trying to do... as well can someone explain what this formula means?

Welcome to PF.

Here is a link that discusses the properties of natural logarithms:
http://en.wikipedia.org/wiki/Natural_logarithm

Perhaps that will help you understand the transform.

 

[baba89]

I can explain what Newton's cooling law is and how to solve it.

Newton's cooling law is a mathematical model that describes the rate at which an object cools down or loses heat to its surroundings. It states that the rate of change of temperature of an object is proportional to the difference between its initial temperature and the temperature of its surroundings. This can be represented by the equation LnT = -kt + LnC, where T represents the temperature of the object, k is a constant, and C is the initial temperature of the object.

To solve this equation, you need to have values for T, k, and C. The ln function is the natural logarithm, and it allows us to solve for T by isolating it on one side of the equation. To do this, you can take the natural log of both sides of the equation, which will give you LnT = Ln(e^-kt) + LnC. From there, you can use logarithm rules to simplify the equation and solve for T.

As for the constant k and the initial temperature C, these can be determined experimentally by collecting data on the temperature of an object over time and plugging those values into the equation. This will allow you to solve for k and C, which can then be used to predict the temperature of the object at any given time.

I hope this explanation helps you understand the formula and how to solve it. If you still have questions, I suggest consulting with your teacher or a tutor for further clarification. Good luck with your lab report!