According to the first law of thermodynamics, U q w . In special cases the statement can be expresse — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

# First Law of Thermodynamics Analysis The first law states: $$\Delta U = q + w$$ where $\Delta U$ = change in internal energy, $q$ = heat absorbed by system, $w$ = work done on system. ## Valid Special Cases: 1. **Adiabatic process** ($q = 0$): $$\Delta U = w$$ - All energy change comes from work only 2. **Isothermal process for ideal gas** ($\Delta U = 0$): $$q = -w$$ - Internal energy unchanged, so heat absorbed equals work done by system 3. **Constant volume process** ($w = 0$): $$\Delta U = q_v$$ - No expansion work, all heat goes to changing internal energy 4. **Cyclic process** ($\Delta U = 0$ overall): $$q_{cycle} = w_{cycle}$$ - Returns to initial state, so net energy change is zero ## Why Option D is Incorrect: Without seeing the specific options, option D likely claims one of these false statements: - $q = w$ (incorrect—they're only equal under specific conditions like isothermal processes, not generally) - $\Delta U = q - w$ (incorrect—sign convention makes this wrong) - $q = \Delta U$ (incorrect—ignores work term) **The key error:** Confusing or misapplying the sign conventions or assuming special case conditions that don't actually apply.