Question

0.5 kg of water at 20 degrees C is added to a container of 1 kg of water at 60 degrees C. 

The water is stirred to even out the temperature. What is the final 

temperature of the water? 

Answer 1

Let $T$ be the final temperature of the water, $T_1$, $m_1$ the temperature and mass of the water that is added, and $T_2, m_2$ the temperature and mass of the water in the container.

Equation of energy balance is $c_w m_1 (T-T_1) + c_w m_2 (T - T_2) = 0$, from where $T = \frac{c_w m_1 T_1 + c_w m_2 T_2}{c_w m_1 + c_w m_2} = \frac{m_1 T_1 + m_2 T_2}{m_1 + m_2} \approx 46.7 ^{\circ}C$