Isometries and embedding of the thermodynamic phase space of an ideal   gas
  In this work we find the Killing vector fields of the riemannian submanifolds of the thermodynamic phase space of an ideal gas and show that the isometry group corresponding to them is homomorphic to the euclidean group $E(2)$. We also give the embedding of these submanifolds in the euclidean space $(R^{3},\ delta)$. 
M. Montesinos-Velasquez