Physics question- Calorimetry

Question

A copper pot with a mass of 0.500kg contains 0.170kg of water, and both are at a temperature of 20 degrees celsius. A 0.250kg block of iron at 85 degrees celsius is dropped into the pot. Find the final temperature of the system, assuming no heat loss to the sorroundings.

Answer 1

The water and the copper gain energy and the iron loses an equal amount

specific heat of water is 4186 J/kgC

specific heat of Copper is 386 J/kgC

specific heat of Iron is 452 J/kgC

T is final temp

Ew = 4186 J/kgC x 0.17 x (T-20)

Ec = 386 J/kgC x 0.5 x (T-20)

Ef = 452 J/kgC x 0.25 x (85-T)

452 J/kgC x 0.25 x (85-T) =  4186 J/kgC x 0.17 x (T-20) + 386 J/kgC x 0.5 x (T-20)

multiply it out and solve for T

113(85-T) =  712 (T-20) + 193(T-20)

9605 - 113T =  712T - 14240 + 193T - 3860

9605 - 113T =  712T - 14240 + 193T - 3860

792T = 27705

T = 35 C

if I didn't make a arith mistake....

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