The efficiency of a furnace’s heat transfer process

In summary, The melting point of aluminium is 660°C and its specific heat capacity (cp) is 0.91 kJ/kgK. The latent heat of melting for aluminium is 321 kJ/kg, modulus of elasticity is 69 GPa, and coefficient of linear expansion is 22.2 x 10-6 /°C. The calorific value for propane is 49.93 MJ/kg and its combustion produces 248 MJ of energy per mole. The ingot cross sectional area is 0.019 m2 and the energy needed to melt it is 907.95 MJ. The energy released by the combustion of propane
  • #1
didaw
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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
 
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  • #2
didaw said:
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?
 
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  • #3
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.
 
  • #4
didaw said:
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.
 
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  • #5
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
 
  • #6
Chestermiller said:
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?
 
  • #7
didaw said:
ah okay so that would be 49.93 x 25 KG = 1248.25 MJ for the energy the propane releases?
Of course.
 
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  • #8
Chestermiller said:
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?
 
  • #9
didaw said:
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.
 
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  • #10
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)
 
  • #11
LeafNinja said:
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)
 
  • #12
didaw said:
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?
 
  • #13
Chestermiller said:
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
 
  • #14
didaw said:
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?
 
  • #15
Chestermiller said:
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?
 
  • #16
didaw said:
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.
 
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  • #17
Chestermiller said:
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!
 

Related to The efficiency of a furnace’s heat transfer process

1. What is the efficiency of a furnace's heat transfer process?

The efficiency of a furnace's heat transfer process refers to the percentage of heat energy produced by the furnace that is actually transferred to the desired location. It is a measure of how effectively the furnace is able to convert fuel into heat.

2. How is the efficiency of a furnace's heat transfer process calculated?

The efficiency of a furnace's heat transfer process is calculated by dividing the amount of heat energy output by the furnace by the amount of fuel energy input. This value is then multiplied by 100 to get a percentage. For example, if a furnace produces 80,000 BTUs of heat energy and consumes 100,000 BTUs of fuel energy, its efficiency would be 80%.

3. What factors can affect the efficiency of a furnace's heat transfer process?

Several factors can affect the efficiency of a furnace's heat transfer process, including the age and condition of the furnace, proper installation and maintenance, the type and quality of fuel used, and the design and insulation of the building where the furnace is located.

4. How can I improve the efficiency of my furnace's heat transfer process?

To improve the efficiency of a furnace's heat transfer process, it is important to have regular maintenance and tune-ups performed by a qualified technician. Additionally, ensuring proper insulation and sealing of ducts and air leaks can help reduce energy loss. Using high-quality fuel and upgrading to a newer, more efficient furnace can also improve efficiency.

5. What are the benefits of having a high efficiency furnace's heat transfer process?

A high efficiency furnace's heat transfer process can bring several benefits, including lower energy bills, reduced environmental impact, and improved comfort in the living space. It can also extend the lifespan of the furnace and reduce the need for frequent repairs or replacements.

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