Thermodynamics

#thermodynamics

1.0

Equations

Force–displacement form

W = Fd

$W$ — work (energy transferred by a force acting through a displacement), joule (J)
$F$ — force, newton (N)
$d$ — displacement, metre (m)

Pressure–volume form

W = P\Delta V

$W$ — work (energy transferred by expansion or compression against an external pressure), joule (J)
$P$ — pressure, pascal (Pa)
$\Delta V$ — change in volume, cubic metre (m³)

Internal energy

\Delta U = U_2 - U_1

$\Delta U$ — change in internal energy (net energy gained or lost by the system as heat and work cross its boundary), joule (J)
$U_2$ — final internal energy of the system, joule (J)
$U_1$ — initial internal energy of the system, joule (J)

Internal energy

\Delta U = \pm q \pm w

$q$ — heat transferred across the system boundary, joule (J)
$w$ — work transferred across the system boundary, joule (J)

Enthalpy

\Delta H = \Delta U + P\Delta V

$\Delta H$ — change in enthalpy (the heat exchanged at constant pressure — internal energy minus the boundary-pushing $P\Delta V$ work not felt as heat), joule (J)
$\Delta U$ — change in internal energy, joule (J)
$P$ — pressure, pascal (Pa)
$\Delta V$ — change in volume, cubic metre (m³)

Second law of thermodynamics

\Delta S = S_2 - S_1

$\Delta S$ — change in entropy (change in the system's disorder — positive for any spontaneous, irreversible process), joule per kelvin (J/K)
$S_2$ — final entropy of the system, joule per kelvin (J/K)
$S_1$ — initial entropy of the system, joule per kelvin (J/K)

Entropy of the surroundings

\Delta S_{surr} = -\dfrac{\Delta H_{sys}}{T_{surr}}

$\Delta S_{surr}$ — change in entropy of the surroundings, joule per kelvin (J/K)
$\Delta H_{sys}$ — change in enthalpy of the system, joule (J)
$T_{surr}$ — temperature of the surroundings, kelvin (K)

Gibbs free energy

\Delta G = \Delta H - T\Delta S

$\Delta G$ — change in Gibbs free energy, joule (J)
$\Delta H$ — change in enthalpy, joule (J)
$T$ — absolute temperature, kelvin (K)
$\Delta S$ — change in entropy, joule per kelvin (J/K)

08 formulas