Water temperature with two materials cooling it

In summary: Energy is still equal everywhere because the system is closed. The final temperature is just the average of the initial temperatures.
  • #1
Stuka_Hunter
11
1
Homework Statement
What is the temperature of water after a long time, if we put 0,50 kg of iron with temperature of 10 °C and 0,30 kg of aluminium with temperature of 20 °C in a bowl of 10 dm3 water with a temperature of 60°C? The heat does not transfer through the walls of the bowl.
Relevant Equations
only one equation given: Q=m*c*change of temperature
I converted dm3 to m3, all the degrees to kelvins and found out the specific heat constants of iron and aluminium (0,45 and 0,91 KJ/kg K), but now i am failing to understand how this was supposed to be calculated. The equation given doesn't really help, as there are two unknowns in it: Q and the change of temperature. Equaling them can't be done, as materials arent the same, in other words, they don't cool down the water at the same rate.

I am struggling with this one, any help is appreciated. :sorry:
 
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  • #2
You are right. You have too many unknowns. That’s 3 equations, one for each material. Is there anything else you know? A couple of readily apparent extra statements that you certainly know.
 
  • #3
Besides the fact that water will cool down unequaly and circulate while cooling down in the bowl, making it cool down faster, no.

Could any of these equations help? We used them with another problem, melting ice.

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  • #4
These things are so obvious and intrinsic to the question that you are overlooking them, but I promise you know them. What can you say about the final temperatures? What can you say about the total energy?
 
  • #5
Well, that is simple. The final temperature will be equal everywhere in the observed system and total energy will also be equal everywhere as a result of this.
 
  • #6
Stuka_Hunter said:
Well, that is simple. The final temperature will be equal everywhere in the observed system and total energy will also be equal everywhere as a result of this.
The system is closed : the energy isn't going anywhere. What exactly do you mean by "total energy will also be equal everywhere" ? that's different from "the final temperature will be equal everywhere".
 
  • #7
Stuka_Hunter said:
Well, that is simple. The final temperature will be equal everywhere in the observed system and total energy will also be equal everywhere as a result of this.

You are right about the temperature. You were given the initial temperatures. They will all wind up at the same unknown final temperature. That means the three delta T’s aren’t three unknowns. They are actually just one unknown. So you have three equations in three unknown delta Qs and one unknown temperature. Three equations in four unknowns. You just need one more equation.

As hmmm27 pointed out “the energy will be equal everywhere” isn’t a sensible statement. Think of those Qs as delta Qs: the amount the thermal energy changes when the temperature changes. Your problem says “the heat does not transfer through the walls.” Does that suggest a relation between all the delta Qs?
 
  • #8
Just to be clear, there's no information missing from the problem statement (except the specific-heat values, which you got from a standard reference).
 

FAQ: Water temperature with two materials cooling it

What factors affect the cooling rate of water with two different materials?

The cooling rate of water with two different materials is affected by several factors, including the type of materials used, the initial temperature of the water, the amount of water, and the surrounding temperature.

How do different materials affect the cooling rate of water?

Different materials have different thermal conductivities, which determines how quickly they can transfer heat. Materials with higher thermal conductivity, such as metal, will cool water more quickly than materials with lower thermal conductivity, such as plastic.

Does the surface area of the materials have an impact on the cooling rate of water?

Yes, the surface area of the materials in contact with the water can affect the cooling rate. A larger surface area allows for more heat transfer, resulting in a faster cooling rate.

At what rate does water cool when using two materials?

The rate at which water cools when using two materials depends on various factors, such as the type of materials, the initial temperature of the water, and the surrounding temperature. Generally, the cooling rate will be faster initially and slow down as the water approaches the temperature of the surrounding environment.

Can using two materials to cool water result in a lower final temperature compared to using one material?

Yes, using two materials with different thermal conductivities can result in a lower final temperature compared to using just one material. This is because the materials work together to transfer heat more efficiently, resulting in a faster cooling rate and a lower final temperature.

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