Thermodynamics ethanol Question

[theLiminator]

Homework Statement

A student mixes 41.8g of ethanol at 15.8 C with 50.7 g of water at 49.2 C. If the resulting temperature of the solution is 28.4 C, what is the specific heat capacity of the ethanol?

Homework Equations

Given heat capacity of water already.

The Attempt at a Solution

let X = heat capacity of ethanol
38.4C = (41.8*15.8*X - 49.2*50.7*4.184)/(X*41.8+50.7*4.184)
i just rearranged and solved for X. I did get the correct answer, however it seems too ugly for a simple MC question.

 

[Borek]

I guess 38.4C is meant to be 28.4C. If so it looks OK to me - that is assuming you got signs right, but if the result is correct you probably did. And I am not aware of a simpler method of getting the answer.

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methods