246 g of hot coffee at 86.0 °C are placed in a 137 g mug at 20.0 °C.The specific heat of coffee is 4.00 J/g °C,while that of the mug is 0.752 J/g °C.Assuming no heat is lost to the surroundings,what is the final temperature of the system: mug + coffee?

Question

Quizplus · Accepted Answer

The final temperature can be found by setting the heat gained by the mug equal to the heat lost by the coffee. Using the formula $q = mc\Delta T$, where $q$ is the heat transferred, $m$ is the mass, $c$ is the specific heat, and $\Delta T$ is the change in temperature, we can set up the equation: $(m_{coffee} \cdot c_{coffee} \cdot (T_f - T_{i,coffee})) + (m_{mug} \cdot c_{mug} \cdot (T_f - T_{i,mug})) = 0$. Solving for $T_f$ gives us the final temperature close to 79.7 °C.

246 G of Hot Coffee at 86