Clausius-Clapeyron Equation: Vapor Pressure & Temperature Relationship, Summaries of Thermodynamics

Download Clausius-Clapeyron Equation: Vapor Pressure & Temperature Relationship and more Summaries Thermodynamics in PDF only on Docsity! A&OS 101 The Clausius-Clapeyron equation Winter, 2008 – Fovell The Clausius-Clapeyron (C-C) equation can be thought of in terms of the Carnot cycle applied to a water vapor/liquid mixture. The system consists of a plunger-equipped piston filled with vapor and liquid in equilibrium (i.e., at saturation). Two adiabatic and two isothermal steps are performed. The isothermal steps involve changes of phase. The system is not isolated with respect to energy transfer – the phase changes will require heat exchange with the environment outside of the piston – but the total mass of water substance is conserved. The figure below sketches a cyclic path on a diagram of saturation vapor pressure and volume. Here, volume refers to the total space occupied by the vapor/liquid mixture in the piston. We presume to know that the saturation vapor pressure is a function only of temperature. Thus, the vertical axis is really temperature. The C-C equation demonstrates this is an exponential relationship. In this cycle, the adiabatic steps involve compression and expansion that push the system out of equilibrium, into a state of subsaturation or supersaturation, and the isothermal steps are the adjustments back to saturation. Suppose we start at A with the saturated mixture occupying volume VA with vapor pressure eSA. If we squeeze the volume a little, down to volume VB, the temperature should go up owing to adiabatic compression. This would make the initially saturated state subsaturated, since the temperature (and thus the saturation vapor pressure) increases. es V A B C D eSA eSB Figure 1: Conceptual es-V diagram for the vapor/liquid Carnot cycle. Not to scale. Variation on vertical axis (effectively temperature) is small; volume variation is huge. So, some liquid has to evaporate for the system to regain equilibrium. During this process, which takes place at constant temperature and saturation vapor pressure, high density (small 1