Categories: Physics, Thermodynamics.

Laws of thermodynamics

The laws of thermodynamics are of great importance to physics, chemistry and engineering, since they restrict what a device or process can physically achieve. For example, the impossibility of perpetual motion is a consequence of these laws.

First law

The first law of thermodynamics states that energy is conserved. When a system goes from one equilibrium to another, the change ΔU\Delta U of its energy UU is equal to the work ΔW\Delta W done by external forces, plus the energy transferred by heating (ΔQ>0\Delta Q > 0) or cooling (ΔQ<0\Delta Q < 0):

ΔU=ΔW+ΔQ\begin{aligned} \boxed{ \Delta U = \Delta W + \Delta Q } \end{aligned}

The internal energy UU is a state variable, so is independent of the path taken between equilibria. However, the work ΔW\Delta W and heating ΔQ\Delta Q do depend on the path, so the first law means that the act of transferring energy is path-dependent, but the result has no “memory” of that path.

Second law

The second law of thermodynamics states that the total entropy never decreases. An important consequence is that no machine can convert energy into work with 100% efficiency.

It is possible for the local entropy SlocS_{\mathrm{loc}} of a system to decrease, but doing so requires work, and therefore the entropy of the surroundings SsurS_{\mathrm{sur}} must increase accordingly, such that:

ΔStot=ΔSloc+ΔSsur0\begin{aligned} \boxed{ \Delta S_{\mathrm{tot}} = \Delta S_{\mathrm{loc}} + \Delta S_{\mathrm{sur}} \ge 0 } \end{aligned}

Since the total entropy never decreases, the equilibrium state of a system must be a maximum of its entropy SS, and therefore SS can be used as a thermodynamic “potential”.

The only situation where ΔS=0\Delta S = 0 is a reversible process, since then it must be possible to return to the previous equilibrium state by doing the same work in the opposite direction.

According to the first law, if a process is reversible, or if it is only heating/cooling, then (after one reversible cycle) the energy change is simply the heat transfer dU=dQ\dd{U} = \dd{Q}. An entropy change dS\dd{S} is then expressed as follows (since S/U=1/T\ipdv{S}{U} = 1 / T by definition):

dS=(SU)V,NdU=dQT\begin{aligned} \boxed{ \dd{S} = \Big( \pdv{S}{U} \Big)_{V, N} \dd{U} = \frac{\dd{Q}}{T} } \end{aligned}

Confusingly, this equation is sometimes also called the second law of thermodynamics.

Third law

The third law of thermodynamics states that the entropy SS of a system goes to zero when the temperature reaches absolute zero:

limT0S=0\begin{aligned} \boxed{ \lim_{T \to 0} S = 0 } \end{aligned}

From this, the absolute quantity of SS is defined, otherwise we would only be able to speak of entropy differences ΔS\Delta S.


  1. H. Gould, J. Tobochnik, Statistical and thermal physics, 2nd edition, Princeton.