106 g of iron at 84.0°C are placed in contact with 205 g of silver at 11.0°C. If no heat is lost to the surroundings, what is the final temperature of the metals? The specific heat of iron is 0.418 J/g·°C and that of silver is 0.251 J/g·°C.

Question

92.0 g of a metal at 92.0°C are added to 53.0 g of water at 30.6°C. When the system reaches constant temperature, the temperature is 38.7°C. What is the specific heat of the metal? The specific heat of water is 4.184 J/g·°C.

Answer 1

heat lost by Fe + heat gained by Ag = 0
[mass Fe x specific heat Fe x (Tfinal-Tintial)] + [mass Ag x specific heat Ag x (Tfinal-Tinitial)] = 0

Substitute and solve for Tfinal.
The second problem is worked the same way.