Question

Temprature of mixture
63.85g piece metall with specific heat capacity of 0,078cal /gK at 89.9 C is dropped into calorimeter with 52.8 ml water solution at 18,4 C

specific heat capacity of water solution is 1,131kcal/lK

finel eqibilirium temrature of the mixture

Answer 1

I assume the density of the solution is 1.0 g/mL which probably is not right. Since the specific heat of the solution is 1.113 cal/g*C which is a deviation from the normal of 1 cal/g*K, I would expect the density to be greater than 1. If your problem gives the density and it is greater than 1.0, then use mass H2O = volume of water x density of water instead of the 52.8 I've used below.

[mass metal x specific heat metal x (Tfinal - Tinitial)] + [mass H2O x specific heat H2O x (Tfinal - Tinitial)] = 0
[63.85 g x 0.078 cal/g*K x (Tfinal - 89.9)] + [ 52.8 g x 1.113 cal/g*C x (Tfinal - 18.4)] = 0
Solve for Tfinal which is the only unknown in the above.