A hot (85.0°C)lump of metal has a mass of 210 g and a specific heat of 0.250 cal/g⋅°C.John drops the metal into a 345-g calorimeter containing 95 g of water at 21.3°C.The calorimeter is constructed of a material that has a specific heat of 0.100 cal/ g⋅°C.When equilibrium is reached,what will be the final temperature? c_water = 1.00 cal/g⋅°C.

Question

Quizplus · Accepted Answer

To find the final temperature, we use the principle of conservation of energy, where the heat lost by the metal and calorimeter equals the heat gained by the water. The equation for heat is $q = mc\Delta T$, where $m$ is mass, $c$ is specific heat, and $\Delta T$ is the change in temperature.Let $T_f$ be the final temperature. The heat lost by the metal is $(210)(0.250)(85 - T_f)$, and the heat lost by the calorimeter is $(345)(0.100)(85 - T_f)$. The heat gained by the water is $(95)(1.00)(T_f - 21.3)$.Setting the heat lost equal to the heat gained and solving for $T_f$ gives us the final temperature.

A Hot (850°C)lump of Metal Has a Mass of 210 G and G