What will be the final temperature of a system in which 150.0 g of water at 5.0°C are added to 1.00 L of water at 90.5°C?
A)106°C
B)5.57°C
C)79.3°C
D)82.8°C

Question

Quizplus · Accepted Answer

To find the final temperature of the system, we use the principle of conservation of energy, assuming no heat is lost to the surroundings. The heat lost by the hot water will equal the heat gained by the cold water. The formula for heat (q) is $q = mc\Delta T$, where $m$ is the mass, $c$ is the specific heat capacity of water (4.18 J/g°C), and $\Delta T$ is the change in temperature. Let $T_f$ be the final temperature.For the 1.00 L of water at 90.5°C (density of water = 1.00 g/mL, so mass = 1000 g), the heat lost is $q_{hot} = 1000 \times 4.18 \times (90.5 - T_f)$.For the 150.0 g of water at 5.0°C, the heat gained is $q_{cold} = 150 \times 4.18 \times (T_f - 5)$.Setting $q_{hot} = q_{cold}$ and solving for $T_f$ gives the final temperature. The calculation confirms that the final temperature is approximately 79.3°C, making option C correct.

What Will Be the Final Temperature of a System in Which