Thermal Properties of Solids and Gases Problem

In summary, at a local county fair, a blacksmith drops a 0.050-kg iron horseshoe into a bucket containing 25.0 kg of water. The initial temperature of the horseshoe is 450°C, and the initial temperature of the water is 23°C. To find the equilibrium temperature of the system, the heat (Q) flowing out of the iron goes into the water, with a negative sign indicating opposite directions. The order of the temperatures, Tf - x versus x - Tf, matters if you want to compare positive values. The final temperature of the system can be determined using the heat capacities of the iron and water. The ring expands only outward when heated because the heat causes molecules to v
  • #1
Silverbolt
24
0
At a local county fair, you watch as blacksmith drops a 0.050-kg iron horseshoe into a bucket containing 25.0 kg of water. If the initial temperature of the horseshoe is 450°C, and the initial temperature of the water is 23°C, what is the equilibrium temperature of the system?


Here is how i am doing it (PLEASE CORRECT ME IF I AM WRONG)

mcΔT= mcΔT
(.050 kg)(448 J/kg(°C) )(Tf-450°C) = (25.0 kg)(4186 J/kg(°C) )(Tf-23°C)
 
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  • #2
It seems perfectly fine to me so far, up to a negative sign, at least.

You should make sure you understand what physics is happening. The heat (Q) flowing out of the iron goes into the water. They have opposite directions (one loses energy in the heat transfer, while the other gains it), so there should be a difference in sign:

QFe = -QH2O

mFecFeΔTFe = -mH2OcH2OΔTH2O

That's the physics. The rest is all computation.

EDIT: you can see that you need the negative sign there just for arithmetic purposes, since the temperature change of the iron is negative, while the temperature change of the water is positive.
 
  • #3
So if I include the negative sign everything else will be correct?
 
  • #4
Your approach is okay, but watch out for the signs of the ΔT's. The order of the temperatures, Tf - x versus x - Tf, matters if you want to compare positive values. Do you expect your final temperature to be higher than 450C?
 
  • #5
Silverbolt said:
So if I include the negative sign everything else will be correct?

Well, I haven't looked to make sure your numbers are correct for the heat capacities, but yes, your method is fine.
 
  • #6
Thank You!
 
  • #7
Please help. When a ring heated why it expands only outward? why not inward also making the hole smaller.
Thank you.
 

What is the difference between solids and gases in terms of thermal properties?

Solids and gases have very different thermal properties. Solids have a fixed shape and volume, meaning their particles are tightly packed and have little room for movement. This results in solids having high thermal conductivity, meaning they can quickly transfer heat energy. Gases, on the other hand, have no fixed shape or volume and their particles are highly spread out. This results in gases having low thermal conductivity, meaning they do not transfer heat energy as quickly as solids.

Why do some materials feel warmer or colder to the touch?

When we touch an object, heat energy is transferred from our hand to the object. The rate at which this heat transfer occurs depends on the thermal conductivity of the material. Materials with high thermal conductivity, such as metals, will feel colder to the touch because they quickly absorb the heat from our hand. Materials with low thermal conductivity, such as wood or plastic, will feel warmer to the touch because they do not absorb heat as quickly.

How do thermal properties affect the behavior of substances?

Thermal properties play a crucial role in determining the behavior of substances. For example, substances with low thermal conductivity, such as insulation materials, are used to trap heat and keep buildings warm. On the other hand, substances with high thermal conductivity, such as metals, are used in cooking as they quickly transfer heat energy. Additionally, thermal expansion, which is the tendency of matter to expand when heated, is also a result of thermal properties and can affect the behavior of substances.

What is the relationship between temperature and thermal properties?

Temperature and thermal properties are closely related. As temperature increases, the movement of particles in a substance also increases, resulting in higher thermal conductivity. This means that materials will transfer heat energy more quickly at higher temperatures. Temperature also affects other thermal properties, such as thermal expansion and specific heat capacity, which are measures of how much a substance will expand or absorb heat energy.

How can we measure thermal properties of solids and gases?

There are various methods for measuring thermal properties of solids and gases. One common method is to use a thermometer to measure temperature changes in a substance. Thermal conductivity can also be measured using specialized equipment, such as a thermal conductivity meter. Other properties, such as specific heat capacity and thermal expansion, can be measured using specific experimental setups and calculations.

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