Thermodynamics Calculators

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Thermodynamics is the branch of physics and chemistry that studies energy transformations — how heat, work, and internal energy relate to one another in systems undergoing change. The four laws define the rules governing all energy exchanges. In biology and biochemistry, thermodynamics determines whether reactions are spontaneous (ΔG < 0), how much energy is available for cellular work, and how proteins fold and membranes form. The Gibbs free energy equation (ΔG = ΔH − TΔS) is the master equation predicting spontaneity at constant temperature and pressure.

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The Four Laws of Thermodynamics

  • Zeroth Law: If A is in thermal equilibrium with B, and B with C, then A is in equilibrium with C. This defines temperature as a measurable quantity.
  • First Law (Conservation of Energy): ΔU = q + w. Energy cannot be created or destroyed; total energy of an isolated system is constant. q = heat; w = work.
  • Second Law: Entropy (S) of the universe always increases in spontaneous processes: ΔS_universe > 0. Disorder increases spontaneously.
  • Third Law: Entropy of a perfect crystal at absolute zero (0 K) is zero.

Gibbs Free Energy

ΔG = ΔH − TΔS

  • ΔG < 0: spontaneous (exergonic)
  • ΔG > 0: non-spontaneous (endergonic)
  • ΔG = 0: equilibrium

Relationship to equilibrium: ΔG° = −RT ln(K_eq). Standard free energy change ΔG° = −RT × ln(K_eq) at 298 K.

Biological Thermodynamics

ATP hydrolysis: ΔG° = −30.5 kJ/mol (standard); in the cell ΔG ≈ −50 kJ/mol (due to low [ADP] and [Pi]). This drives endergonic reactions by coupling. Protein folding: driven by hydrophobic effect (entropy gain from releasing ordered water), H-bonds, and van der Waals interactions — overall ΔG_folding ≈ −20 to −60 kJ/mol (modest — explains why proteins can denature).

Glossary

Gibbs Free Energy (ΔG)
ΔG = ΔH − TΔS; determines spontaneity at constant T and P; ΔG<0 = spontaneous; ΔG=0 = equilibrium; related to equilibrium constant by ΔG° = −RT ln(K_eq).
Entropy (S)
A thermodynamic state function measuring disorder or the number of microstates available to a system; the second law states that ΔS_universe > 0 for all spontaneous processes.
First Law of Thermodynamics
Energy is conserved: ΔU = q + w; energy transforms between heat, work, and internal energy but cannot be created or destroyed in any isolated system.

Frequently Asked Questions

Zeroth law: thermal equilibrium is transitive — defines temperature as a physical property. First law: energy is conserved (ΔU = q + w); energy converts between forms but is never created or destroyed. Second law: entropy of the universe increases in spontaneous processes (ΔS_univ > 0); heat spontaneously flows from hot to cold; organized states become disordered. Third law: entropy of a perfect crystal at absolute zero (0 K) equals zero — provides an absolute reference for entropy. The laws apply universally to all physical and chemical processes.

ΔG = ΔH − TΔS. ΔG < 0 = spontaneous (the reaction releases usable energy and can occur without external input). ΔG > 0 = non-spontaneous (requires energy input). ΔG = 0 = equilibrium. ΔG depends on both enthalpy (ΔH, heat released or absorbed) and entropy (ΔS, disorder change). A reaction can be spontaneous even if endothermic (ΔH > 0) if it has a large positive ΔS and/or high temperature. Conversely, exothermic reactions (ΔH < 0) can be non-spontaneous if they have a large negative ΔS at low temperature.

ΔG° = −RT ln(K_eq), where R = 8.314 J/mol/K and T is in Kelvin. This connects thermodynamics to equilibrium chemistry: a large negative ΔG° gives K_eq >> 1 (products strongly favored); ΔG° = 0 gives K_eq = 1 (equal amounts); large positive ΔG° gives K_eq << 1 (reactants favored). At 25°C (298 K), every 5.7 kJ/mol change in ΔG° changes K_eq by 10-fold. In the cell, ΔG is not ΔG° — actual concentrations differ from standard (1 M): ΔG = ΔG° + RT ln([products]/[reactants]).

Living organisms appear to decrease local entropy — building complex proteins, DNA, and cellular structures from simple precursors. This does not violate the second law because organisms are open systems that must export entropy to their surroundings. Every biosynthetic reaction that decreases internal entropy is coupled to reactions that release more entropy (heat, waste CO₂) to the environment. The net entropy of the universe still increases. A cell maintains low entropy by consuming high-enthalpy nutrients (food) and releasing low-enthalpy waste products and heat, increasing surroundings entropy more than it decreases internal entropy.