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Lecture9Ch161Feb23

# Lecture9Ch161Feb23 - Summary of last lecture The meaning of...

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Summary of last lecture The meaning of TD potentials - minimum at proper conditions Stability conditions and their possible violations Joule-Thompson process (Throttling) reports on intermolecular interactions

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Key Concepts and Lessons: a) Canonical vs Microcanonical ensemble b) Boltzmann Distribution- derivation c) Canonical Partition function and its relation to TD d) Grand Canonical partition Function Reading: Reif, Ch6
A Practical Example: Throttling Throttling is used to cool gases and convert them to liquids. How does it work? Here gas is being ‘’squeezed’’ through a porous partition. The walls are insulated so that no heat is exchanged with outside world. Now we note that gas passing from left to right actually makes some work (apparently at the expense of its own internal energy). Let us do some bookkeeping of this work. Imagine mass M of gas passing from left to right. Before crossing the plug it had volume V 1 and was under pressure p 1 . After passing the plug it has volume V 2 and pressure p 2 . What work W does it do? Well gas displaces V 2 under pressure p 2 on the right I.e. it does work p 2 V 2 . Is that all? No- because gas itself is being pushed out from left hand side and gas on the left does work on our mass M which is p 1 V 1.. So the total work as mass M pushes through is W=p 2 V 2 -p 1 V 1

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Throttling, Cont The work done is at the expense of energy (lost or gained) and we have: dQ = dE + W = 0 E 2 E 1 + p 2 V 2 p 1 V 1 = 0 or finally: H 2 = E 2 + p 2 V 2 = H 1 = E 1 + p 1 V 1 Throttling is an isoenthalpic process! How does T change at throttling? These are prototypical constant enthalpy curves and their slopes show whether changing pressure is heating or cooling gas!
Throttling, Cont Now we want to determine the effect of throttling on gas T. To this end we want to evaluate = T p H we have the usual relation: dH = TdS + Vdp = T S p T dp + S T P dT + Vdp = 0 i.e. C p dT + T S p T + V dp = 0 T p H = T S p T dp + V C p using Maxwell relation S p T = V T P = V α we get finally: μ = V C p T α 1 ( )

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Does T increase or decrease at throttling? For an ideal gas μ = 0 Prove:5pts Which means that T effect of throttling is directly related to intermolecular forces which act between particles! This opens an opportunity to explore intermolecular forces by analyzing throttling experiments. I will prove later that generally the equation of state for a non-ideal gas
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Lecture9Ch161Feb23 - Summary of last lecture The meaning of...

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