Solving the differential equation of ideal gas condition at isoprocesses

In this article we consider a special method of description the space of conditions of ideal gas. It is based on the solution of quasilinear partial differential equation of the fist order. Geometrically the solution of this equation represent a surface in the space of thermodynamic variables $(Q, v, p)$. We solve this equation using method of characteristics which are defined by the system of the ordinary differential equations. We received the general solution's formula, and also its variants for the cases of isochoric, adiabatic and isothermic processes. Cauchy problem for the said differential equation is connected with finding of the integrated surface passing through the set curve of any process which can be presented in a parametrical form. We describe such process as time functions. It is given the geometrical representation of the space of ideal gas conditions at isoprocesses. We construct the following integrated surfaces using means of computer mathematics.