Q.$200\ \text{g}$ of water at $80\,^\circ\text{C}$ is poured into $300\ \text{g}$ of water at $20\,^\circ\text{C}$ inside a calorimeter of negligible heat capacity. Find the common temperature reached by the mixture once thermal equilibrium is established.

Calorimetry is the measurement of the amount of heat released or absorbed by a thermodynamic system during a heating process. When a hot body is brought into contact with a cold body and no heat is allowed to escape to the surroundings, the heat lost by the hot body exactly equals the heat gained by the cold body: $Q_{gain} = -Q_{lost}$, or equivalently $Q_{gain}+Q_{lost}=0$ (heat lost taken as negative, heat gained as positive). This is usually measured using a calorimeter, an insulated vessel of water fitted with a thermometer and a stirrer. If a sample of mass $m_1$ and specific heat $s_1$ at temperature $T_1$ is dropped into water of mass $m_2$, specific heat $s_2$, at temperature $T_2$, both reach a common final (equilibrium) temperature $T_f$. Using $Q_{gain}=m_2s_2(T_f-T_2)$ and …