An ideal gas is contained in a piston-cylinder arrangement. The walls of the cylinder and the piston itself are "adiabatic", i.e. no heat energy can be exchanged between the piston-cylinder and its surroundings. The piston experiences friction as it moves. All the heat generated by the friction however is trapped inside the cylinder (and therfore it adds heat energy to the gas). By the firts law of theromodynamics the energy balance can be written in differential form as: dU=dQ-dW dU - change of the gase's internal energy, dQ - heat energy added to the gas, (for adiabatic case dQ=0, however for the case presented here dQ would come from the friction of the piston with the cylinder wall) dW - work done by gas. Assuming that the inital vol, temp. and pressure are V0, T0 and P0 respectively, how could you express the relation petween pressure and volume of this system at any given point of the expansion? For example, the relation between the pressure and volume in a similar scenario but WITHOUT friction is given by the well known thermodynamic equation of: PV^k = Constant, where k=Cp/Cv (Here Cp and Cv are the gas's molar heat capacity under constant pressure and constant volume respectively).