Calculate heat required to melt ingot

[Parsifal1]

Homework Statement

Given that aluminium has a specific heat of 0.9KJ/KgK, a melting point of 660 degrees Celsius and a latent heat of fusion of 390KJ/Kg, calculate the heat energy required to melt a 10Kg ingot, starting from a room temperature of 20 degrees Celsius.

Homework Equations

dQ= m c dt
q=Lm m

The Attempt at a Solution

(10)(0.9)(640)=5760KJ

I get a different answer using the latent heat equation, so which should be used for working out the heat energy for melting and why are both specific and latent heat given, if not as a redherring?

 

[Chestermiller]

If you heat the ingot to 660C using 5760 kJ, has it melted yet?

 

[DrClaude]

Is heating the ingot to 660 °C sufficient to melt it?

Please note that the prefix kilo is written with a lowercase k.

 

[Parsifal1]

Is heating the ingot to 660 °C sufficient to melt it?

Please note that the prefix kilo is written with a lowercase k.

660 is the melting point of aluminium. If it is the case that the first equation is sufficient then what is with the fact that they mention latent heat aswell?

 

[DrClaude]

Is it sufficient to bring a substance to its melting point for it to melt? What is the definition of latent heat?

 

[SteamKing]

660 is the melting point of aluminium. If it is the case that the first equation is sufficient then what is with the fact that they mention latent heat aswell?

Do you understand what latent heat of fusion means?

 

[Parsifal1]

Do you understand what latent heat of fusion means?

'The specific latent heat of fusion, l, of a substance is the heat needed to change a mass of 1 kg the substance from a solid at its melting point into liquid at the same temperature.'

So I need to add the heat to raise it to boiling point to the heat to melt it?

5760kJ+(390000*10)=3905760000J

 

[DrClaude]

'
So I need to add the heat to raise it to boiling point to the heat to melt it?

5760kJ+(390000*10)=3905760000J

Yes, but check those units.

 

[SteamKing]

'The specific latent heat of fusion, l, of a substance is the heat needed to change a mass of 1 kg the substance from a solid at its melting point into liquid at the same temperature.'

So I need to add the heat to raise it to boiling point to the heat to melt it?

5760kJ+(390000*10)=3905760000J

Yes.

But you've made some kind of silly mistake in the calculation above.

The heat required to raise the aluminum to the melting point (not the boiling point) is 5760 kJ. Once the aluminum is at the melting point, it takes 390 kJ/kg to turn solid aluminum into molten aluminum.

 

[Parsifal1]

Yes.

But you've made some kind of silly mistake in the calculation above.

The heat required to raise the aluminum to the melting point (not the boiling point) is 5760 kJ. Once the aluminum is at the melting point, it takes 390 kJ/kg to turn solid aluminum into molten aluminum.

5760000+(360000*10)=9660000J

 

[SteamKing]

5760000+(360000*10)=9660000J

That looks much better, except it's 390000 * 10, not 360000.

Always proofread your work to avoid silly mistakes like this.

 

[jeneng]

Homework Statement

Given that aluminium has a specific heat of 0.9KJ/KgK, a melting point of 660 degrees Celsius and a latent heat of fusion of 390KJ/Kg, calculate the heat energy required to melt a 10Kg ingot, starting from a room temperature of 20 degrees Celsius.

Homework Equations

dQ= m c dt
q=Lm m

The Attempt at a Solution

(10)(0.9)(640)=5760KJ

I get a different answer using the latent heat equation, so which should be used for working out the heat energy for melting and why are both specific and latent heat given, if not as a redherring?

First of all need to convert dt degree Celcius to Kelvin and calculate

8218.35 KJ is the correct answer

 

[Chestermiller]

First of all need to convert dt degree Celcius to Kelvin and calculate

8218.35 KJ is the correct answer

Why do you feel that you need to convert C to K in this problem.

Also, your answer is incorrect. Please show your work.

Also, you realize that this thread is over 5 years old, right? And the OP hasn't logged into Physics Forums for 3 years, right? And, in his final post, the OP got the correct answer.

 

[docnet]

I have a question. Does any textbook explain the latent heat of fusion using quantum theory, or have heat and temperature always been classical entities in physics?

 

[DrClaude]

I have a question. Does any textbook explain the latent heat of fusion using quantum theory, or have heat and temperature always been classical entities in physics?

You can understand it using statistical physics. There is no particular need to invoke quantum mechanics.

 

[Mikkel-ES]

If I understand this correctly; 1 kg aluminium requires aproximatly 1MJ to go from room temperature to liquid form?

So if I would like to make a thermal battery out of aluminium with the thermal capasity of 1MWh ( 1MWh = 3600 [s/h] * 1 [MWh] = 3600 MJ = 3,6 GJ), I would need 3,6 Ton of aluminium?

Inspiration from this youtube video: