Water temperature with two materials cooling it

[Stuka_Hunter]

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.

 

[Cutter Ketch]

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.

 

[Stuka_Hunter]

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.

 

[Cutter Ketch]

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?

 

[Stuka_Hunter]

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.

 

[hmmm27]

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".

 

[Cutter Ketch]

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?

 

[hmmm27]

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).