Specific heat/equilibrium in three component system (Thermo)

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Homework Help Overview

The discussion revolves around a thermodynamics problem involving the specific heat and equilibrium temperature in a three-component system. The original poster presents an equation based on heat transfer and expresses confusion regarding the lack of mass values provided in the problem statement.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore how to express the equilibrium temperature in terms of symbols for masses and specific heats, questioning the necessity of numerical values. There is discussion about simplifying the equation by relating all masses and specific heats to one reference mass and specific heat.

Discussion Status

Some participants have provided guidance on how to approach the problem by suggesting the use of symbolic representation for masses and specific heats. The conversation indicates a productive direction, with participants clarifying the requirements of the problem and addressing assumptions about temperature units.

Contextual Notes

There is mention of a cropped portion of the problem that specifies a numerical value is needed, along with a reference to using a binomial expansion, which some participants find unclear. The original poster notes the absence of mass values as a point of confusion.

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Homework Statement


Rather than retyping the problem, I've uploaded a screenshot here >> http://imgur.com/EB5MrtP

Homework Equations


Q_1 + Q_2 + Q_3 ... = 0
mc \Delta T = Q

The Attempt at a Solution


a. Q_{tea} + Q_{met} + Q_{cr} = 0

I converted the temperatures to K, so T_{cr} and T_{met} = 293.15K, while T_{tea} = 373.15K

Constructing the equation, I got:

0 = (m_{met} * c_{met}* (T_{equil}-293.15)) + (m_{cr} * c_{cr} * (T_{equil}-293.15)) + (m_{tea} * c_{tea} * (T_{equil} - 373.15))

I'm stuck here now, because the problem doesn't give any of the masses, it only relates them to each other. The specific heats I can find because the specific heat of water is a known value, but I'm stuck on the masses. What am I missing?
 
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I believe the problem is asking you to express the equilibrium temperature in terms of the symbols for the masses and specific heats. If so, you do not need to plug in numerical values for these quantities.
 
TSny said:
I believe the problem is asking you to express the equilibrium temperature in terms of the symbols for the masses and specific heats. If so, you do not need to plug in numerical values for these quantities.

Oh, there's a small part at the bottom that got cropped out, it specifically asks for a numerical value. It also mentions something about using a binomial expansion to solve it, which I didn't understand how it applied to this problem. I've amended the link in the OP with the fixed version.
 
OK. Sorry, I did not see part (c) when I first looked at the problem.

Try expressing all masses in terms of one of the masses, say ##m_{met}##. Likewise, express all specific heats in terms of one of the specific heats, say ##c_{met}##.

You will then find that the equation simplifies such that you do not need any numerical values for the masses or specific heats.

Also, you do not need to express the temperatures in K. You can keep them in oC because you are dealing with temperature differences here.
 
Oh, duh, I see it now. Thank you! I probably should have tried that first, but I just didn't think of it.
 

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