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5_60_lecture19

# 5_60_lecture19 - MIT OpenCourseWare http/ocw.mit.edu 5.60...

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MIT OpenCourseWare http://ocw.mit.edu 5.60 Thermodynamics & Kinetics Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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5.60 Spring 2008 Lecture #19 page 1 Clausius-Clapeyron Equation Let’s revisit solid-gas & liquid-gas equilibria. We can make an approximation: >> gas solid liquid gas vap subl , V VV We can ignore the molar volume of the condensed phase compared to the gas. Taking the Clapeyron equation (exact), e.g. for solid-gas eq. and using the approximation above: ∆∆∆ == ≈ ∆∆ subl subl subl gas subl subl SH H dp dT VT VTV Assuming an ideal gas, = gas RT p == subl subl 22 ln pH dpp d = This is the Clausius-Clapeyron Equation for liq-gas, replace sub with vap i.e. vap vap ln = The Clausius-Clapeyron equation relates the temperature dependence of the vapor pressure of a liquid or a solid to vap or sub (respectively).
5.60 Spring 2008 Lecture #19 page 2 We can make another approximation: Assuming subl H independent of T , 22 11 subl subl subl 2 21 2 12 1 1 ln pT HH dp p TT dT pR R ⎛⎞ ∆∆ == = ⎜⎟ ⎝⎠ ∫∫ 1 2 This is the Integrated Clausius-Clapeyron Equation ( f o r l i q - g a s , r e p l a c e sub with vap ) i . e .

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5_60_lecture19 - MIT OpenCourseWare http/ocw.mit.edu 5.60...

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