How Much Energy and Power Are Required to Weld Carbon Steel?

[Fowler_NottinghamUni]

Homework Statement

Given, the density, specific heat per unit volume, latent heat of fusion, melting point and thermal conductivity - calculate the energy needed to melt a cubic mm of carbon steel, starting at 20 celcius.

Hence find the minimum power needed to generate a bead on a plate weld of 15 mm square cross sectional area at a welding speed of 4mm/s.

Homework Equations

density ro = 7900 kg/m^3
specific heat per unit mass Cm = 0.45kJ/Kg/K
Melting Temperature of Carbon steel Tm= 1535 deg C
Latent heat of melting deltaHf = 270 kJ/Kg
deltaT = Tm-starting temp

The Attempt at a Solution

Am I right in saying that there are two energies, one to heat the metal up and another energy to overcome the latent heat of fusion?

If so, I used Q = (mXCmxdeltaT) + (mxdeltaHf).

When substituting the numbers I got out 7.5 J, which seems a little low.
As for the second part, I'm not sure how to go about it.
If anyone is any the wiser please let me know where I have gone wrong?!

Many thanks, Gavin.

 

[KataKoniK]

Dear Gavin,

Your approach to finding the energy needed to melt a cubic mm of carbon steel is correct. However, the result of 7.5 J seems low because you have used the specific heat per unit mass instead of the specific heat per unit volume. Since the given density is in kg/m^3, you need to use the specific heat per unit volume, which is given as 0.45 kJ/m^3/K.

Therefore, the correct equation is Q = (VxCVxdeltaT) + (VxdeltaHf), where CV is the specific heat per unit volume and V is the volume of the cubic mm (1 mm^3). Substituting the given values, we get Q = (1x0.45x(1535-20)) + (1x270) = 689.5 J.

For the second part, we need to find the minimum power needed to generate a bead on a plate weld. To do this, we can use the formula P = Q/t, where Q is the energy calculated above and t is the welding time. Since the welding speed is given as 4 mm/s, the welding time for a 15 mm square cross sectional area would be 15/4 = 3.75 s.

Therefore, the minimum power needed would be P = 689.5/3.75 = 183.86 W.

I hope this helps. Let me know if you have any further questions. Good luck with your calculations!

 

[piercas]

Thank you for sharing your attempt at solving the problem. Your approach is correct, but there may be some errors in your calculations. Let's go through the solution step by step to ensure accuracy.

Firstly, you are correct in saying that there are two energies involved in melting the carbon steel - the energy needed to raise the temperature from 20 degrees Celsius to the melting point (1535 degrees Celsius) and the energy needed to overcome the latent heat of fusion. So, the total energy needed is the sum of these two energies.

The equation you have used is correct - Q = (m x Cm x deltaT) + (m x deltaHf). However, there are a few things to note here. Firstly, the specific heat given is per unit mass, so you need to multiply it by the mass to get the specific heat per unit volume. Secondly, the melting point given is in degrees Celsius, so you need to convert it to Kelvin for the equation to be correct. So, the correct equation would be:

Q = (m x ro x Cm x deltaT) + (m x deltaHf)

Where:
m = mass of the steel in cubic mm
ro = density in kg/m^3
Cm = specific heat per unit volume in kJ/Kg/K
deltaT = difference in temperature in Kelvin (Tm - starting temp)
deltaHf = latent heat of fusion in kJ/Kg

Now, let's substitute the values given in the problem:
m = 1 mm^3 = 1 x 10^-9 m^3
ro = 7900 kg/m^3
Cm = 0.45 kJ/Kg/K
deltaT = 1535 + 273 - 20 = 1788 K
deltaHf = 270 kJ/Kg

Plugging these values into the equation, we get:
Q = (1 x 10^-9 x 7900 x 0.45 x 1788) + (1 x 10^-9 x 270) = 6.75 J

So, the correct energy needed to melt a cubic mm of carbon steel starting at 20 degrees Celsius is 6.75 J, which is close to your answer of 7.5 J.

Now, for the second part of the problem, we need to find the minimum power needed to generate a bead on a plate weld of