Question

A 20g of iron metal at 85C is placed in an insulated container with 80g of water at 4C.

a) Calculate the final temperature of the system (the answer is 6.1 C, please show the steps to get this answer).

b) Calculate the entropy change for the iron-water system. Is the result in accord with the Second Law of Thermodynamics?

Answer 1

Using the thermodynamic equation

q gain = q loss

(mass)*(change in temperature)*(specific heat of iron) = (mass)*(change in temperature)*(specific heat of iron)

Mass of iron = 20g, ii) Temperature of iron = 85oC, iii) specific heat of iron = 0.450 J/g-K, iv) mass of water = 80g, v)Temperature of water = 4oC, vi) specific heat of water = 4.184 J/g-K

(20g)*(85 - x)*(0.450J/g-K) = (80g)*(x - 4)*(4.184 J/ g-K)

9 (85 - x) = 334.72(x - 4)

765 - 9x = 334.72x - 1338.88

334.72 x + 9 x = 1338.88+765

343.72 x = 2103.88

x = 2103.88 / 343.72

x = 6.1oC

The final temperature is 6.1oC