Properties of Matter — Thermal & Advanced Practice (Hard)

Quick Recap — Thermal Properties & Advanced Problems

• Expansion: linear $\Delta L=\alpha L\,\Delta T$; area $\beta=2\alpha$; volume $\gamma=3\alpha$. Clamped rod thermal force $=YA\alpha\,\Delta T$.
• Calorimetry: $Q=mc\,\Delta T$ (sensible), $Q=mL$ (latent); mixtures reach equilibrium by heat lost $=$ heat gained. Water: $L_f=80$ cal/g, $L_v=540$ cal/g.
• Conduction: $\dfrac{Q}{t}=\dfrac{kA\,\Delta T}{L}$; thermal resistance $\dfrac{L}{kA}$ adds in series. Series junction of equal-$A$, equal-$L$ rods: $T_j=\dfrac{k_1T_1+k_2T_2}{k_1+k_2}$.
• Radiation: Stefan $P\propto AT^4$; Wien $\lambda_{max}T=$ const; Newton's cooling: rate $\propto(T-T_s)$.

Worked mini-example. 50 g of ice at $0^\circ$C is added to 50 g of water at $40^\circ$C. Heat available $=50\times40=2000$ cal melts only $\dfrac{2000}{80}=25$ g of ice, so equilibrium is at $0^\circ$C with $25$ g of ice still unmelted.