How to Use Clausius-Clapeyron Equation
The Clausius-Clapeyron equation describes the transition between two phases of matter for a particular substance. This transition can be shown with a pressure-temperature (P-T) diagram. This type of graph shows pressure on the y-axis and temperature on the x-axis. The coexistence curve shows the points on the P-T diagram where a particular substance is changing between phases of matter. The Clausius-Clapeyron equation gives the slope of the coexistence curve at each point.
Instructions
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1
Describe the Clausius-Clapeyron mathematically. This is given as dP/dT = L/TdV where "dP" is the instantaneous change in pressure at temperature "T" and "dT" is the instantaneous change in temperature at temperature "T." "L" is the latent heat of the substance, "T" is the temperature and "dV" is the instantaneous change in volume at the phase transition point for temperature "T."
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2
Interpret the value dP/dT. The instantaneous change in pressure divided by the instantaneous change in temperature at temperature gives us the slope of the coexistence curve at temperature "T." In other words, the value dP/dT tells us how fast the phase transition is changing at "T."
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3
Derive the Clausius-Clapeyron equation for the liquid and vapor phase. Using the ideal gas law and integral calculus, we can use the Clausius-Clapeyron equation to approximate the relationship between two temperatures on the coexistence curve.
This equation is given as follows: in (P1/P2) = dHvap/R(1/T2 -- 1/T1) where the points (T1, P1) and (T2, P2) are two points on the coexistence curve. dHvap is the molar enthalpy of vaporization, which is a constant for that substance. "R" is the universal gas constant of 8.314 J mol'1K'1. -
4
Apply the form of the Clausius--Clapeyron equation obtained in Step 3. The equation in (P1/P2) = dHvap/R(1/T2 -- 1/T1) is commonly used to predict the transition pressure "P2" at some temperature "T2" from a known transition point (P1,T1).
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