There is a rod that is split into two sections. The left side is copper with value of 390, temp of 100 degrees c and the length is 2m. The right side is silver, 420, temp 20 degrees celsuis, and length 1m.

Question

There is a rod that is split into two sections. The left side is copper with value of 390, temp of 100 degrees c and the length is 2m. The right side is silver, 420, temp 20 degrees celsuis, and length 1m.

I need to calculate the temperature.

390 X 1 X 100-t / 2 = 420 X 1 X t-20 / 1

Is this how I would set it up to solve for the temp?

Thank you.

Answer 1

What are your 390 and 420 "values" and what are their units?

What temperature are you solving for? is this supposed to be a steady state problem?

Answer 2

I believe that 390 is the coefficient of thermal conductivity "κ" from

dQ/dt = κ•A•dT/dx.
The units of "κ" are watts/K• meters. Its value for cooper is 390.
As for the rest I'm in complete accord with drwls: what temperature ....

Answer 3

To solve for the temperature, we can set up an equation using the principle of heat transfer, also known as the heat equation. The equation states that the heat gained by one object is equal to the heat lost by another object when they are in thermal contact. The general form of the heat equation is:

Q1 = Q2

In this case, let's denote the left side (copper) as Object 1 and the right side (silver) as Object 2. The heat transfer is given by:

Q1 (heat gained by the copper) = Q2 (heat lost by the silver)

Now, let's break down the heat transfer equations for each object:

For Object 1 (copper):
Q1 = mass1 × specific heat capacity1 × change in temperature1

For Object 2 (silver):
Q2 = mass2 × specific heat capacity2 × change in temperature2

In this case, we have the following information:

Mass1 = 390 (value of copper)
Specific heat capacity1 = 1 (assuming it's in J/g°C, where 1 g = 1 cm^3 for simplicity)
Change in temperature1 = (temperature of copper - unknown temperature)

Mass2 = 420 (value of silver)
Specific heat capacity2 = 1 (assuming it's in J/g°C, where 1 g = 1 cm^3 for simplicity)
Change in temperature2 = (unknown temperature - temperature of silver)

Now, let's put it all together:

Q1 = Q2
mass1 × specific heat capacity1 × change in temperature1 = mass2 × specific heat capacity2 × change in temperature2

390 × 1 × (100 - T) = 420 × 1 × (T - 20) / 2

Note that we divide the right side by 2 because the length of the copper rod is twice the length of the silver rod (2m vs. 1m).

By rearranging and solving this equation, we would be able to find the unknown temperature 'T'.