GChem question from Destroyer

[healthcaree]

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Question:
An unknown metal of 50g is intially at 100˚C and dropped into a beaker of 200g of water at 30˚C. The final temperature of the system is 40˚C. Find the specific heat of the metal if the specific heat of water is 4.2 J/g ˚C.

Answer: 2.8 J/g ˚C


Heat lost by metal = Heat gained by H2O

mcΔT = mcΔT

(50)c(60) = (200)(4.2)(10) <--- having a problem here..

3000c = 8400

thus, c=2.8 J/g &#730;C


for the &#916;T for heat lost by metal.. don't we always calculate the delta portion as final minus the initial? (40-100)

metal LOST heat which makes it -60, not +60?
heat gained by H2O seems to be +10, which is final-initial (40-30) giving a positive value of 10.

a negative value wasn't an option, so luckily i got this problem right.. but was just wondering how it works. i'm sure would've gotten it wrong if -2.8 was one of the options.

can someone help me out here? thanks.

 

[silveryhair]

I also lucked out on this problem. But I figured it out:

It actual equation not listed is q(rxn) = q(water) + q(metal)
Then you know that the q(rxn) is zero because it is at equilibrium.

So then you subtract the q(metal) from the equation to equal:

(-)m(metal)c(metal)&#916;T = mc&#916;T (water)

And solve...

Question:
An unknown metal of 50g is intially at 100&#730;C and dropped into a beaker of 200g of water at 30&#730;C. The final temperature of the system is 40&#730;C. Find the specific heat of the metal if the specific heat of water is 4.2 J/g &#730;C.

Answer: 2.8 J/g &#730;C


Heat lost by metal = Heat gained by H2O

mc&#916;T = mc&#916;T

(50)c(60) = (200)(4.2)(10) <--- having a problem here..

3000c = 8400

thus, c=2.8 J/g &#730;C


for the &#916;T for heat lost by metal.. don't we always calculate the delta portion as final minus the initial? (40-100)

metal LOST heat which makes it -60, not +60?
heat gained by H2O seems to be +10, which is final-initial (40-30) giving a positive value of 10.

a negative value wasn't an option, so luckily i got this problem right.. but was just wondering how it works. i'm sure would've gotten it wrong if -2.8 was one of the options.

can someone help me out here? thanks.