Mass of object during heat exchange

This conversation is about summarization and not answering questions. In summary, the conversation discusses finding the mass of iron in a mixture of aluminum and water, assuming no heat loss to the surroundings. The solution involves using the heat capacities of the materials and the change in temperature to set up an equation and solve for the mass of iron. The question also touches on the topic of heat transfer by conduction. Another individual joins the conversation seeking help on a different topic, but is advised to start a new thread following the forum rules.
  • #1
v3ra
21
0

Homework Statement



An aluminum container with a mass of 400 g contains 200 g of water at a temperature of 18°C. After a block of iron at a temperature of 90°C is placed in the water, the final temperature of the mixture changes to 28°C. Find the mass of the iron, assuming that there is no loss of heat to the surroundings.


Homework Equations



mass of aluminum = 0.40 g, heat capacity of aluminum = 910 J(kg.°C)
mass of water = 0.20 g, heat capacity of water = 4200 J
mass of iron = ? heat capacity of iron = 460 J

(delta)t = change in temperature

mAcA(delta)tA +mWcW(delta)tW + mIcI(delta)tI = 0



The Attempt at a Solution



This is the solution shown in the book:

(0.40 kg) x (910 J/(kg.°C)) x (28°C - 18°C) + (0.20 kg) x (4200 J/(kg.°C)) x (28°C - 18°C) + (mI) x (460 J/(kg.°C)) x (28°C - 90°C) = 0

3640 + 8400 - 28520 mI = 0
12040 = 28250 mI
mI = 0.422 kg


What I want to know is where they got 3640 and 8400 from, when 0.40 x 910 = 364 and 0.20 x 4200 = 840. Why did they add a zero? Is this an error in the book? I also do not know where 28 520 is from. What am I missing...
 
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  • #2
(0.40 kg) x (910 J/(kg.°C)) x (28°C - 18°C) = 0.4 * 910*10 = 3640

You are forgetting to multiply by the change in temperature i.e. 10.
 
  • #3
a block of aluminum 4 inch by 4 inch have and chamber of 1inch x 1 inch witch is heat faster the chamber or the whole block?
 
  • #4
You should start a new thread with your question with all the relevant equations and terms in it. Otherwise, you are hijacking another person's thread which I think your question is not related to the OP's question.
 
  • #5
Hi Rock.freak667 what you mean I am hijacking onother person's thead,
I just like to find out if a 1inch diameter long 4 inch heat faster then all aluminum block
the block as reach the temperature of 100F can you help me ?
 
  • #6
maya2323 said:
Hi Rock.freak667 what you mean I am hijacking onother person's thead,

It means that you are posting a question in another person's thread which has nothing to do with your question.

I advise you to start a new thread following the template so that you can input your question and what equations you think will be relevant.

maya2323 said:
I just like to find out if a 1inch diameter long 4 inch heat faster then all aluminum block
the block as reach the temperature of 100F can you help me ?

If you are at a loss with what equation would be relevant, look up heat transfer by conduction, as that is what you are essentially wanting to know.
 
  • #7
Thanks lot but do you know the answer? can you send to me? thanks
 
  • #8
maya2323 said:
Thanks lot but do you know the answer? can you send to me? thanks

As per the forum rules, no on at PF can just give you the answer. You need to show some attempt at finding the answer. Once more, please start a new thread.
 

1. What is the definition of "mass of object" in relation to heat exchange?

The mass of an object refers to the amount of matter it contains, typically measured in kilograms (kg). In the context of heat exchange, the mass of an object is important because it affects the amount of heat that is required to raise its temperature.

2. How does the mass of an object affect the amount of heat it can hold?

The mass of an object is directly proportional to the amount of heat it can hold. This means that the greater the mass of an object, the more heat it can absorb or release before its temperature changes significantly.

3. Is the mass of an object constant during heat exchange?

In most cases, the mass of an object remains constant during heat exchange. This is because the amount of matter in an object does not change unless there is a chemical reaction or phase change occurring. However, in some cases, a small amount of matter may be lost or gained due to evaporation or condensation of a substance.

4. How does the specific heat capacity of an object relate to its mass during heat exchange?

The specific heat capacity of an object is a measure of the amount of heat required to raise the temperature of one kilogram of the object by one degree Celsius. Therefore, the mass of an object is directly proportional to its specific heat capacity. Objects with a higher mass typically have a higher specific heat capacity, meaning they require more heat to raise their temperature compared to objects with a lower mass.

5. Can the mass of an object affect the rate of heat exchange?

Yes, the mass of an object can affect the rate of heat exchange. Objects with a higher mass will generally take longer to heat up or cool down compared to objects with a lower mass. This is because it requires more heat energy to raise the temperature of a larger mass compared to a smaller mass.

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