Small solids embedded in gaseous protoplanetary disks are subject to strong dust-gas friction. Consequently, tightly-coupled dust particles almost follow the gas flow. This near conservation of dust-to-gas ratio along streamlines is analogous to the near conservation of entropy along flows of (dust-free) gas with weak heating and cooling. We develop this thermodynamic analogy into a framework to study dusty gas dynamics in protoplanetary disks. We show that an isothermal dusty gas behaves like an adiabatic pure gas; and that finite dust-gas coupling may be regarded as an effective heating/cooling. We exploit this correspondence to deduce that 1) perfectly coupled, thin dust layers cannot cause axisymmetric instabilities; 2) radial dust edges are unstable if the dust is vertically well-mixed; 3) the streaming instability necessarily involves a gas pressure response that lags behind dust density; 4) dust-loading introduces buoyancy forces that generally stabilizes the vertical shear instability associated with global radial temperature gradients. We also discuss dusty analogs of other hydrodynamic processes (e.g. Rossby wave instability, convective overstability, and zombie vortices), and how to simulate dusty protoplanetary disks with minor tweaks to existing codes for pure gas dynamics.
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