Question

A chunk of nickel weighing 19.7 grams and originally at 97.88 °C is dropped into an insulated cup containing 77.0 grams of water at 22.27 °C. Assuming that all of the heat is transferred to the water, the final temperature of the water is______ °C.

Answer 1

specific heat capacity of nickel = 0.440 J/g.oC

specific heat capacity of water = 4.184 J/g.oC

Let us denote Ni by symbol 1 and H2O by symbol 2

m1 = 19.7 g

T1 = 97.88 oC

C1 = 0.44 J/goC

m2 = 77.0 g

T2 = 22.27 oC

C2 = 4.186 J/goC

T = to be calculated

Let the final temperature be T oC

use:

heat gained by 2 = heat lost by 1

m2*C2*(T-T2) = m1*C1*(T1-T)

77.0*4.186*(T-22.27) = 19.7*0.44*(97.88-T)

322.322*(T-22.27) = 8.668*(97.88-T)

322.322*T -7178.1109 = 848.4238 - 8.668*T)

T= 24.25 oC

Answer: 24.25 oC