$1.000\;kg$ water at $0^oC$ are mixed with $0.100\;kg$ water at $90^oC$. Knowing that the mixture was made in an $400\;g$ iron container containing initially the warm water, calculate the final temperature.
The energy is conserved: Heat received by the cold water = Heat lost by the warm water and the container Let be $x$ the final temperature: $4184\cdot 1\cdot (x-0)$ $=$ $- 4184\cdot 0.1\cdot (x$ $-$ $90)$ $-$ $470\cdot 0.4\cdot (x$ $-$ $90)$ $x \approx 11.4^oC$