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

💡 Solution & Explanation

I need to identify what the mathematical expression **ΔU = q + w** represents. ## Step-by-step Solution: **Step 1: Identify the symbols** - $\Delta U$ = change in internal energy of a system - $q$ = heat energy exchanged by the system - $w$ = work done on/by the system **Step 2: Recognize the fundamental principle** This is **the First Law of Thermodynamics**, which states that the total energy change of an isolated system equals the sum of heat and work interactions. **Step 3: Energy conservation basis** The equation reflects energy conservation: - Internal energy can increase or decrease - This change comes from two sources: heat transfer ($q$) and mechanical work ($w$) **Step 4: Sign conventions** - $q > 0$: heat absorbed by system - $q < 0$: heat released by system - $w > 0$: work done **on** the system - $w < 0$: work done **by** the system ## Answer: $\Delta U = q + w$ is the mathematical expression for the **First Law of Thermodynamics** (or the Law of Conservation of Energy in thermodynamic form). It states that the change in internal energy of a system equals the net heat absorbed plus the net work done on the system.