- #1

lufbrajames

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## Homework Statement

We need to know the temperature of the copper bit of a soldering iron varies with time after the power has been switched on. This is a first step to determine how long it takes for the temperature of the bit to reach the operating temperature at which it can melt the solder. We assume all heat produced goes directly to the bit and none is lost to the air. i.e. the temperature of the bit, Theta = Theta (t), depends only on time.

3 laws of physics:

the rate of energy storage in the bit is the product of the mass m of copper, the specific heat c of copper and the rate of change in the bit.

the rate of loss of heat from the bit to the air has the form kA(theta - Thate a) where theta a is the temprature of the air, A is the (constant) cross section of the bit, and k is a constant

The heat traveling from the barrel to the bit is the sum of the heat loss from the bit and the heat stored in the bit (consesrvation of energy)

1) To which value do you expect the temprature of the bit to settle?

2) Sketch a graph of Theta with t (time)

3) Write down the differential equation which describes the cooling process.

4)Given that the solution tof the equation

dtheta/dt + a theta = b

where a and b are cpnstant, is

theta = b/a + Ce^-at

where c is a constant, write down the solution of your eqaution in part 3 which satisfies the initial condition theta = theta 0 at t = 0

## Homework Equations

## The Attempt at a Solution

1) the temperaturewill settle at theta a the temperature of the air.

2)i drew a graph that showed the temperature drop rapidly at first and then steadyout to nearly level at theta a

3) (this is where i get really stuck!) i got the following

dtheta/dt + k = A(theta - theta 0)

4)

theta = A(theta - theta 0) / k

thanks for any help you can give =)