U q w , is mathematical expression for — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

# Solution: $\Delta U = q + w$ (First Law of Thermodynamics) **Step 1: Identify the symbols** - $\Delta U$ = change in internal energy of the system - $q$ = heat absorbed by the system - $w$ = work done on the system **Step 2: Apply the First Law of Thermodynamics** The First Law states that energy is conserved. The change in internal energy equals the total energy input: $$\Delta U = q + w$$ **Step 3: Sign convention** - $q > 0$: heat absorbed by system (endothermic) - $q < 0$: heat released by system (exothermic) - $w > 0$: work done on the system (compression) - $w < 0$: work done by the system (expansion) **Step 4: Physical meaning** The internal energy of a system changes when: - Heat flows in/out ($q$ term), OR - Work is performed on/by the system ($w$ term) This is the **fundamental relationship** between thermodynamic quantities and represents energy conservation in chemistry.