$200 \ g$ of hot water at $80^{\circ}C$ is added to $300\ g$ of cold water at $10^{\circ}C$. Neglecting the heat taken by the container, calculate the final temperature of the mixture of water. Specific heat capacity of water = $44200\ J kg^{-1} K^{-1}$.

Using the principle of heat exchange, the heat lost by the hot water equals the heat gained by the cold water. Setting the specific heats equal gives 200 * (80 - T) = 300 * (T - 10), which expands to 16000 - 200T = 300T - 3000. Solving this equation yields 500T = 19000, so the final temperature is 38 degrees Celsius.

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