Question

Chemical potential in a thermodynamic system is a measure of:

• A. The change in pressure with volume at constant temperature
• B. The change in entropy with temperature at constant volume
• C. The potential energy per particle to do work
• D. The energy change when a particle is added to a system at constant temperature and pressure

Hint:

Chemical potential tells you how much the system’s energy changes when you add a particle—key in chemical reactions, phase changes, and diffusion.

Answer 1

The Correct Option is D

Step 1: Chemical potential (\( \mu \)) is a fundamental thermodynamic quantity that describes how the energy of a system changes with the addition of particles.
Step 2: Mathematically, it is defined as: \[ \mu = \left( \frac{\partial G}{\partial n} \right)_{T,P} \] where \( G \) is the Gibbs free energy, \( n \) is the number of moles, \( T \) is temperature, and \( P \) is pressure.
Step 3: This means chemical potential quantifies the change in free energy when an infinitesimal amount of substance is added, holding temperature and pressure constant. It governs processes like diffusion, phase equilibrium, and chemical reactions.
Why the other options are incorrect:

• (A) This refers to an isothermal compressibility concept, not chemical potential.
• (B) This refers to specific heat, not chemical potential.
• (C) While it may sound close, chemical potential is more formally defined via energy change with respect to particle number, not just “potential energy”.