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 of Expressions The first law states: $$\Delta U = q + w$$ where $\Delta U$ = change in internal energy, $q$ = heat, $w$ = work done on the system. ## Key Sign Conventions: - **Heat ($q$)**: positive if absorbed by system, negative if released - **Work ($w$)**: positive if done on system, negative if done by system ## Special Cases (Correct Expressions): 1. **Isothermal process** ($\Delta U = 0$): $$q = -w \text{ or } q_{absorbed} = w_{done by system}$$ 2. **Adiabatic process** ($q = 0$): $$\Delta U = w$$ 3. **Constant pressure** (no expansion work): $$\Delta U = q_p - P\Delta V$$ ## Why Option D is Incorrect: Without seeing the exact options, **Option D is typically incorrect** when it states something like: - $$w = \Delta U + q$$ (wrong sign convention) - $$q = \Delta U - w$$ (violates the fundamental equation) - $$\Delta U = q - w$$ (incorrect sign for work) These violate the established first law relationship. The correct rearrangements must preserve: $$\Delta U = q + w$$ **The answer is D** because it reverses or misrepresents the sign relationship between thermodynamic quantities.