Thread: I am trying to find out two unknown values from one equation

Does anyone know how to find two unknown values in the one equation it is for a year twelve maths b assignment. I am trying to find out what c and k are in this equation (by the way c and k are constants):
T=TS + ce^(-kt)
Where TS= Temperature of surroundings which equals 23 degrees
T= Temperature of the body at a time (t)
t= Time
c & k= constants
Thank you for your help.

Originally Posted by SOS

Does anyone know how to find two unknown values in the one equation it is for a year twelve maths b assignment. I am trying to find out what c and k are in this equation (by the way c and k are constants):
T=TS + ce^(-kt)
Where TS= Temperature of surroundings which equals 23 degrees
T= Temperature of the body at a time (t)
t= Time
c & k= constants
Thank you for your help.

You need data, say some times , and the corresponding tempratures .

RonL

thanks ronL, in class we got the time and temperature which is:
t= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
T= 93 75 62 51 45 41 37 35 33 31 30 29 28 27.8 27
But even if I substitute those numbers in I still have two unknowns left, and I don't know what to do after I substitute T and t in.
Thank you for your help

Originally Posted by SOS

Does anyone know how to find two unknown values in the one equation it is for a year twelve maths b assignment. I am trying to find out what c and k are in this equation (by the way c and k are constants):
T=TS + ce^(-kt)
Where TS= Temperature of surroundings which equals 23 degrees
T= Temperature of the body at a time (t)
t= Time
c & k= constants
Thank you for your help.

Check your problem again...these types of problems usually come with initial conditions such as

when t= y=

ok umm.. this is the question in full:
"Newton's Law of Cooling states that the rate of change of temperature of a body is proportional to the difference in temperature between the body and the temperature of its surrounds."
(I don't actually understand the above sentence is that what you mean by t= y=)
"The formula fo Newton's law of cooling is:
T=TS + ce^(-kt)
Where TS= Temperature of surroundings which equals 23 degrees
T= Temperature of the body at a time (t)
t= Time
c & k= constants"
I then have made a graph of time (t) verse temperature (T) when t=x and T=y
It then says to
"Determine how well Newton's Law of Cooling models your experimental data. Your solution should include the use of a spreadsheet and a comparative graph."
So I thought that it meant that I had to come up with values for the constants so that I could model the formula against the data I obtained in a graph.
Thanks for your help.

Originally Posted by SOS

thanks ronL, in class we got the time and temperature which is:
t= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
T= 93 75 62 51 45 41 37 35 33 31 30 29 28 27.8 27
But even if I substitute those numbers in I still have two unknowns left, and I don't know what to do after I substitute T and t in.
Thank you for your help

You wish to fit a curve of the form:



to this data.

Rearrange:



Now take logs to get:



so plot against , this should be a straight line and its slope will be , and the intercept .

RonL