Calorimetry Problem...PLEASE HELP

[starrz329]

Ok the question is...

Pour 125g of water which is at 75 C into a calorimeter cup which already has 125g of water at 25 degrees C. The specific heat of water is 4.184 J/gC. Assume the styrofoam cup has a heat capacity constant of 41.84 J/C. Calculate the final temprature Tf.

PLEASE HELP!!!

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[shaqkillz451]

I think the key is to figure out how to predict the temperature changes. Since the water at the higher temp will lose heat, write its temp change as (75-Tf) and the water which gains heat will be (Tf-25). The point of stating the use of a calorimeter is only to imply that no heat is lost from system. So then use the formula heat gained=heat lost or mc(deltaT)=mc(deltaT). So the equation is,

125g(75-Tf)4.184J/gC = 125g(Tf-25)4.184J/gC

mass and specific heat cancel out, so you're left with

75-Tf = Tf-25--> Tf = 50 degrees Celsius.

Answer makes sense, since the final temp should be between the two initial.

***Others please confirm check this!