Problem — Copper calorimeter

Problem

We pour $400$ g of water at $50\ ^{\circ}$C into a copper calorimeter initially at $20\ ^{\circ}$C. The equilibrium temperature is $47.5\ ^{\circ}$C. Determine the calorimeter’s heat capacity. ($c_{\text{water}}=4186\ \mathrm{J/(kg\cdot K)}$).

The hot water poured into the copper calorimeter reaches thermal equilibrium.

Solution

Setting up. The water releases heat, the calorimeter absorbs it. With $C_{cal}$ the calorimeter’s heat capacity: $m_w\,c_w\,(T_e-50)+C_{cal}\,(T_e-20)=0$ Substitution: $0.4\cdot 4186\cdot(47.5-50)+C_{cal}\,(47.5-20)=0$ $-4186+27.5\,C_{cal}=0$ $\ev{C_{cal}=\frac{4186}{27.5}\approx 152\ \mathrm{J/K}}$

Links

Topics: Termologia Concepts: Calore specifico e capacità termica Skills: Equazione calorimetrica Objects: Calorimetro