A 100.0 g sample of water at 27.0°C is poured into a 77.4 g sample of water at 89.0°C. What will be the final temperature of the water?
A) 88.7°C
B) 424°C
C) 23.6°C
D) 185°C
E) 54.1°C

Question

Quizplus · Accepted Answer

The final temperature of the water can be found using the principle of conservation of energy, where the heat lost by the warmer water is equal to the heat gained by the cooler water. The formula used is $m_1c\Delta T_1 = -m_2c\Delta T_2$, where $m_1$ and $m_2$ are the masses of the two water samples, $c$ is the specific heat capacity of water (which is 4.18 J/g°C and cancels out in this equation), and $\Delta T$ is the change in temperature. Solving for the final temperature gives a result of 54.1°C, indicating that when the two samples reach thermal equilibrium, the final temperature of the mixture is 54.1°C.

A 1000 G Sample of Water at 27