An aluminum cup contains 225 g of water and a 40 g copper stirrer, all at 27°C. A 450 g sample of silver at an

Question

An aluminum cup contains 225 g of water and a 40 g copper stirrer, all at 27°C. A 450 g sample of silver at an initial temperature of 89°C is placed in the water. The stirrer is used to stir the mixture gently until it reaches its final equilibrium temperature of 32°C. Calculate the mass of the aluminum cup.

Answer 1

Assuming the entire system is insulated to prevent any heat energy from leaving the system the calculations proceed as follows


Q=mc∆T

Total Q is unchanged

c(water)=4.1813 m(water)=0.225 kq
c(copper)=0.385 m(copper)=0.040 kg
c(alum.)=0.897 m(alum.)=x
c(silver)=0.0559 m(silver)=0.450 kg

(0.225)(4.1813)(5)+(0.385)(0.040)(5)+x(0.897)(5)=(0.450)(0.0559)(5)

collecting and solving

x=1.04 kg