Q.Explain calorimetry and derive an expression for final temperature when two thermodynamic systems are mixed.

Step 1. Calorimetry is the measurement of the heat released or absorbed by a system during a heating process. When a hot body is placed in contact with a cold body inside an insulated container (no heat escapes to the surroundings), the heat lost by the hot body equals the heat gained by the cold body: $Q_{gain}=-Q_{lost}$.

Step 2. Let a sample of mass $m_1$, specific heat $s_1$, initially at temperature $T_1$, be dropped into calorimeter water of mass $m_2$, specific heat $s_2$, initially at temperature $T_2$, and let $T_f$ be the common final (equilibrium) temperature.

Step 3. From the definition of specific heat capacity: $Q_{gain}=m_2s_2(T_f-T_2)$ (heat gained by the water) and $Q_{lost}=m_1s_1(T_f-T_1)$ (heat lost by the hot sample). Equating: $m_2s_2(T_f-T_2)=-m_1s_1(T_f-T_1)$. …

• Sign errors when equating heat lost/gained -- remember $Q_{lost}$ is written as a positive quantity being SUBTRACTED, or a …