Answer:
The final temperature of the water system is 51.5 °C.
Explanation:
A 50.0 gram sample of water initially at 100 °C
Mass of the water = 50 g
Initial temperature of the water = [tex]T_i=100[/tex]
Final temperature of the water after mixing = [tex]T_f=[/tex]
-Q' = heat lost by 50.0 g of water
[tex]-Q'=mc\Delta (T_f-T_i)[/tex]
A 100.0 gram sample of water initially at 27.32°C
Mass of the water ,m'= 10.00 g
Initial temperature of the water = [tex]T_i'=100[/tex]
Final temperature of the water after mixing = [tex]T_f=[/tex]
Q = heat gained by 100.0 g of water after mixing
[tex]Q=m'c\Delta (T_f-T_i')[/tex]
-Q'=Q (Energy remains conserved)
[tex]-(mc\Delta (T_f-T_i))=m'c\Delta (T_f-T_i')[/tex]
[tex]-(50 g\times 4.184J/g^oC(T_f-100^oC))=100 g\times 4.184J/g^oC(T_f-27.32^oC)[/tex]
[tex]T_f=51.54^oC\approx 51.5^oC[/tex]
The final temperature of the water system is 51.5 °C.
