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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