Question

A piece of iron (Cp = 0.450 J/(gi°C)) that has a mass of 21.5 g and an initial temperature of 100.0°C is submerged in X g of water (Cp = 4.184 J/(gi°C)) at 20.0°C. The temperature of the system (iron and water) changes to 21.4°C. What is the value of X?

Answer 1

from here:

http://www.chemteam.info/Thermochem/MixingMetal&Water.html

a) The colder water will warm up (heat energy "flows" in to it). The warmer metal will cool down (heat energy "flows" out of it).
b) The whole mixture will wind up at the SAME temperature. This is very, very important.
c) The energy which "flowed" out (of the warmer water) equals the energy which "flowed" in (to the colder water)

qlost=qgain
substituting values
(21.5) (100.0 - 21.4)(0.45) = (X) (21.4- 20.0) (4.184)