Thermodynamics

• Average or Individual Molar Heat Capacity?
  Learn when to use individual or average molar heat capacities, with formulas for pure substances, mixtures, temperature ranges, and reactions.
• How Does Adiabatic vs. Isothermal Compression Affect Gas Work?
  For the same ideal gas and compression ratio, reversible adiabatic compression requires more work than isothermal compression because the gas heats up.
• 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.
• Do Quantum Energy Generators Produce More Energy Than They Use?
  Quantum energy generators have not been shown to create net energy. Learn how conservation laws and careful input-output tests assess such claims.
• 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.
• What Is Chemical Potential in Thermodynamics?
  Chemical potential is the free-energy cost of adding matter. Learn its definitions, units, equilibrium role, and an ideal-gas example.
• Can a Liquid Boil in a Closed Container?
  A liquid can boil in a closed container, but heating usually raises the pressure too, changing its boiling temperature and creating a rupture hazard.
• How Much Ice Is Needed to Cool Water by a Given Temperature?
  Calculate the ice mass needed to cool water by a chosen amount using a heat balance that includes melting and warming the melted ice.
• Why Is Magnesium Not Used to Reduce Alumina Industrially?
  Magnesium can reduce alumina in principle, but its volatility, reaction-control challenges, and cost make the process impractical compared with electrolysis.
• What Is a State Function, and How Can You Identify One?
  A state function depends only on a system’s equilibrium state, not its history. Learn how endpoint comparisons and exact differentials identify one.
• Why Are Intensive Properties Not Additive?
  Intensive properties do not add because they describe a system's state rather than its total amount; see how scaling and mixing determine combined values.
• Why Is Entropy an Extensive Quantity?
  Entropy is extensive because independent subsystems have multiplying numbers of microstates, and the logarithm turns that product into a sum.