Isotherms of Real Gas

 This model illustrates the process of isothermal compression in a real gas (consider water vapor as an example) over a wide range of temperatures. The isotherms are shown on the P-V plane. Any substance can be transformed from one physical state to another. There are three common physical states: solid, liquid, and gaseous. Transition between states is referred to as a phase change. Evaporation and condensation are examples of phase change. Any real gas can be turned into a liquid under certain conditions. Isotherms of a real gas are significantly different from the isotherms of an ideal gas. A liquid and its vapor in a closed vessel can coexist in a dynamic equilibrium as long as the number of molecules leaving the liquid is equal to the number of molecules returning to the liquid state from the vapor state. Such systems are known as two-phase system. The vapor in equilibrium with its liquid is known as a saturated vapor. The pressure of a saturated vapor is a function of temperature only, and is independent of its volume. Therefore, an isotherm of a real gas on the (P,V) diagram exhibits a horizontal section that corresponds to the two-phase state. The pressure and density of a saturated gas increase with temperature, while the density of a liquid decreases due to the thermal expansion. Consequently, at a certain temperature, the densities of gas and liquid will be the same. The temperature at which this phenomenon occurs is referred to as the critical temperature Tcr. When T ≥ Tcr, there appears to be no physical difference between the liquid and its saturated vapor. The critical temperature of water is 647.3 K. The critical temperature of nitrogen it is 123 K. At room temperature (~300 K), water exists in equilibrium with its vapor, while nitrogen exists in gaseous state only. Change the temperature of the process and observe the ensuing results on the dependency graph p(V). The horizontal region on this graph corresponds to the two-phase system. The energy diagram displays the quantity of heat Q added to the system, the work done W, and the change ΔU in the system's internal energy resulting from the isothermal expansion (compression) of water vapors. You can set the temperature to be higher than the critical temperature, in which case the isotherm will be represented above the two-phase region. Note the disappearance of the plane part of the curve that corresponds to the liquid condensation phase. Determine the critical temperature by modifying the gray curve that binds the two-phase region.