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Combined Law of Thermodynamics

For an infinitesimally small change in the state of a closed system, the first law of thermodynamics can be expressed as the following differential equation:

dU = dQ + dW

where U is the internal energy of the system, Q is the amount of the heat received (absorbed) by the system, and W is the work done on the system.

If the process is also reversible, the second law of thermodynamics and entropy are related through the following mathematical relationship:

dS ≥ dQ / T


dQ ≤ T·dS

where T is the absolute temperature.

For a reversible adiabatic process (Q = 0) the work is given as

dW = P·dV

The first law of thermodynamics (dU = dQ + P·dV) and the second law of thermodynamics (dQ ≤ T·dS) can now be subsumed into a single mathematical expression, referred to as the combined law of thermodynamics:

dU - T·dS + P·dV ≤ 0

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