Calculus
posted by Anonymous
I do not understand what this question is asking and how to get the result for it:
"Suppose we have a metal bar of length L0 metres at temperature T0 in degrees Celsius.When the bar is heated or cooled, the length of the bar changes. The amount that the length changes is proportional to the product of the temperature change and the original length of the bar L0. Let á be the proportionality constant of this change where the units for á is measured in m/m◦C (metres per metres degree Celsius). Find an expression for the length L of the metal bar as a function of the temperature T.Draw a sketch of the graph of this function, labelling the point where T = 0."
So far I have figured that you have to have these values of length and temperature proportional to each other so like when length increases, the temperature decreases and as length decreases the temperature increases. But I do not know how to write that and how to come about drawing the graph.

Steve
Well, let's see what they have said.
dL = k dT L0
so,
L = k*L0*T + C
Now you can plug in initial conditions or boundary conditions to determine k and C
Respond to this Question
Similar Questions

heat
A siler bar 0.125 meter long is subjected to a temperature change from 200 degrees celsius to 100 degrees celsius what willbe the length of the bar after the temperature change? 
Physical Science
Hello, I wanted to know if I came to the correct answer in the following problem... Thank You I used: I=LK(ToTf) LD=LI A silver bar 0.125 meter long is subjected to a temperature change from 200 degrees celsius to 100 degrees celsius. … 
Physical Science
Hello, I wanted to know if I came to the correct answer in the following problem... Thank You I used: I=LK(ToTf) LD=LI A silver bar 0.125 meter long is subjected to a temperature change from 200 degrees celsius to 100 degrees celsius. … 
calculus
A cold metal bar at 30 degrees Celsius is submerged in a pool maintained at a temperature of 40 degrees Celsius. Half a minute later, the temperature of the bar is 20 degrees Celsius. How long will it take the bar to attain a temperature … 
AP Calculus AB
the temperature of a 10m long metal bar is 15 degrees celcius at one end and 30 degrees celcius on the other end. Assuming that the temperature increases linearly from the cooler end to the hotter end, what is the average temperature … 
Physics
A conduction heat wave is caused to pass through a metal bar of average temperature Tmean = 36 degrees altering its temperature sinusoidally with an amplitude of Ti=2 degrees. The equation which gives the temperature T(x.t) of the … 
chemistry
a 225.0 g sample of an unknown, silver, pure metal was heated to 95.5 degrees celsius then put into 150.50 g of water at 22.5 degrees celsius. the water was heated by the hot metal to a temperature of 31.4 degrees celsius. what is … 
science
a silver bar 0.125 meter long is subjected to a temperature change from 2oo degrees celsius to 100 degrees Celsius what will the length of the bar be after the temperature change 
Calculus I
Suppose we have a metal bar of length L0 metres at temperature T0 in degrees Celsius.When the bar is heated or cooled, the length of the bar changes. The amount that the length changes is proportional to the product of the temperature … 
Physics/Science
A steel bar reaches a temperature of 420 degrees celsius after it has been welded. Over the next 50 minutes the steel bar cools to 30 degrees celsius. What is the rate of temperature change of the iron?