Internal energy

• Given Constant Temperature, Why Can Pressure Affect Internal Energy?
  At constant temperature, ideal-gas internal energy stays fixed, but pressure can change a real fluid’s volume and intermolecular potential energy.
• How to Derive a Thermodynamic Relation from Helmholtz Free Energy
  Starting from Helmholtz free energy, derive pressure and entropy identities and show why (∂U/∂V)T = T(∂P/∂T)V − P.