The efficiency of a furnace’s heat transfer process

[didaw]

Homework Statement

A smelting furnace is fuelled with propane gas to melt Aluminium ingots for a wheel manufacturing. The furnace is loaded up with 50 aluminium ingots each of mass 20 kg. If 25 kg of propane is used to complete the melting process calculate the efficiency of the furnace’s heat transfer process.

Relevant Equations

Calculate the energy that must be supplied by the furnace to melt the ingots completely. Before being placed in the furnace the ingots are stored at 15°C.
mc(t2-t1) + ML
1000(910)(660-15)+1000(321000) = 907.95 MJ

If I am honest with you I don't even know where to start, if someone wouldn't mind helping me find a starting point?

Additional information
Melting point of aluminium 660°C
Specific heat capacity for aluminium (cp): 0.91 kJ/kgK
Latent heat of melting for aluminium (L): 321 kJ/kg
Modulus of elasticity for aluminium: 69 GPa
Coefficient of linear expansion for aluminium: 22.2 x 10-6 /°C
Calorific value for propane 49.93 MJ/kg
Ingot cross sectional area 0.019 m2

 

[haruspex]

dont even know where to start

Yet you have managed to find the energy needed to melt the ingots.
Can you find the energy the propane releases?

 

[didaw]

The combustion of propane produces 248 of energy per mole.
1000kg in moles is 55509.3 so would that be 248*5509.3=1366306.4 am I on the right track with that or is that irrelevant?
Also 1 mole of any gas at S.T.P is 22.4 liters. I am not to sure if that is relevant or not sorry I am very new to all of this and i feel like I've been dropped in the deep end.

 

[Chestermiller]

The combustion of propane produces 248 of energy per mole.
1000kg in moles is 55509.3 so would that be 248*5509.3=1366306.4 am I on the right track with that or is that irrelevant?
Also 1 mole of any gas at S.T.P is 22.4 liters. I am not to sure if that is relevant or not sorry I am very new to all of this and i feel like I've been dropped in the deep end.

They tell you to use 49.93 MJ/kg for the propane.

 

[didaw]

may have got that wrong, propane formula C3H8 12 moles in carbon 0.99 moles in hydrogen (12x3)+(0.99x8) = 43.92 per g 43.92 x 1000000 = 43920000

 

[didaw]

They tell you to use 49.93 MJ/kg for the propane.

ah okay so that would be 49.93 x 25 KG = 1248.25 MJ for the energy the propane releases?

 

[Chestermiller]

ah okay so that would be 49.93 x 25 KG = 1248.25 MJ for the energy the propane releases?

Of course.

 

[didaw]

Of course.

I am not really to sure how to tackle this but if the heat of melting 1 KG of ally is 321 that would be 321 kJ x 1000 KG = 321000 kJ = 321 MJ so 1248.25 - 321 = 927.25 MJ would that be the answer or is that the heat wasted?

 

[LeafNinja]

I am not really to sure how to tackle this but if the heat of melting 1 KG of ally is 321 that would be 321 kJ x 1000 KG = 321000 kJ = 321 MJ so 1248.25 - 321 = 927.25 MJ would that be the answer or is that the heat wasted?

You are calculating Heat In - Heat Used to melt ots which is not efficiency

From my understading efficieny is $\frac{what\ you\ want}{what\ you\ put\ in}$

In this case that would be $\frac{heat\ to\ increase\ temperature\ +heat\ used\ to\ melt\ ingots}{heat\ in\ from\ melting\ propane}$

Because what you want is any heat that contributes to melting the ingots and what you put in is the heat generated through the chemical reaction.

You have already calculated these values as 907.95 MJ and 1248.25 MJ.

 

[didaw]

would the heat to increase temperature be 660 the melting point of the ally so 660 + 907.95 / 1248.25 = 1.256118566 MJ (im presuming the answer is going to be in MJ)

 

[didaw]

You are calculating Heat In - Heat Used to melt ots which is not efficiency

From my understading efficieny is $\frac{what\ you\ want}{what\ you\ put\ in}$

In this case that would be $\frac{heat\ to\ increase\ temperature\ +heat\ used\ to\ melt\ ingots}{heat\ in\ from\ melting\ propane}$

Because what you want is any heat that contributes to melting the ingots and what you put in is the heat generated through the chemical reaction.

You have already calculated these values as 907.95 MJ and 1248.25 MJ.

would the heat to increase temperature be 660 the melting point of the ally so 660 + 907.95 / 1248.25 = 1.256118566 MJ (im presuming the answer is going to be in MJ)

 

[Chestermiller]

would the heat to increase temperature be 660 the melting point of the ally so 660 + 907.95 / 1248.25 = 1.256118566 MJ (im presuming the answer is going to be in MJ)

I have no idea what this is supposed to mean?

 

[didaw]

I have no idea what this is supposed to mean?

I think that I am getting confused with the sum leafninja gave me 'what you want/what you put in = heat to increase temperature+heat used to melt ingots/heat in from propane' as heat to increase temperature i used the melting point of the ally 660 (I think this is wrong) then the heat used to melt the ingots would be 907.95 mj /heat of the propane 1248.25 mj what = 1.256118566 MJ

 

[Chestermiller]

I think that I am getting confused with the sum leafninja gave me 'what you want/what you put in = heat to increase temperature+heat used to melt ingots/heat in from propane' as heat to increase temperature i used the melting point of the ally 660 (I think this is wrong) then the heat used to melt the ingots would be 907.95 mj /heat of the propane 1248.25 mj what = 1.256118566 MJ

How can 907.95 divided by 1248.25 be 1.25?

 

[didaw]

How can 907.95 divided by 1248.25 be 1.25?

i did 660+907.95/1248.25 (660 for the heat that is required to melt a ingot but I am pretty sure that i went wrong their) should i have done 907.95/1248.25 to get the answer?

 

[Chestermiller]

i did 660+907.95/1248.25 (660 for the heat that is required to melt a ingot but I am pretty sure that i went wrong their) should i have done 907.95/1248.25 to get the answer?

You already used the 660 once in getting the 907.25 (see post #1). How many times do you plan on using it?

Yes, the efficiency is 907/1248.

 

[didaw]

You already used the 660 once in getting the 907.25 (see post #1). How many times do you plan on using it?

Yes, the efficiency is 907/1248.

Thank you!