  We first review the general class of accelerating, rotating and charged
Plebanski-Demianski (PD) black holes in presence of cosmological constant,
which includes the Kerr-Newman rotating black hole and the Taub-NUT spacetime.
We assume that the thermodynamical pressure may be described by the negative
cosmological constant and so the black hole represents anti-de Sitter (AdS) PD
black hole. The thermodynamic quantities like surface area, entropy, volume,
temperature, Gibb's and Helmholtz's free energies of the AdS PD black hole are
obtained due to the thermodynamic system. Next we find the critical point and
corresponding critical pressure, critical temperature and critical volume for
AdS PD black hole. Due to the study of specific heat capacity, we obtain ${\cal
C}_{V}=0$ and ${\cal C}_{P}\ge 0$. From this result, we conclude that the AdS
PD black hole may be stable. We examine the Joule-Thomson expansion of PD black
hole and by evaluating the sign of Joule-Thomson coefficient $\mu$, we
determine the heating and cooling nature of PD black hole. Putting $\mu=0$, we
find the inversion temperature. Next we study the heat engine for AdS PD black
hole. In Carnot cycle, we obtain the work done and its maximum efficiency. Also
we describe the work done and its efficiency for a new engine. Finally, we
analyze the efficiency for the Rankine cycle in PD black hole heat engine.
