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# 1. (35 points) by Qet = QoQ = Q0Q2 N!37 N/A (1-B, (r), where A- B(T) V * 4R (e-(R)/KT - 1) R dR

## 1. (35 points) by Qet = QoQ = Q0Q2 N!37 N/A (1-B, (r), where A- B(T) V * 4R (e-(R)/KT - 1) R dR is the second virial coefficient. The classical partition function for an imperfect gas comprising N atoms is given approximately VN 1. h = and (2mk&T)/2 In Qd a) Derive a general expression for the energy E = kT of the imperfect gas in N,V terms of B2(T) and/or dB(T)/dT. You may use the same approximation we used in class when finding In(Q2). b) The Lennard-Jones potential is given by u(R) = 4 [ 12 For this potential, R B(T) = 2 3 16 . Find an expression for AE/E, the fractional correction to the ideal 9kBT gas energy Eo, where AE, which will depend on and , is the contribution from the Lennard- Jones interaction. c) For a pair of Ar atoms, the Lennard-Jones parameters are =3.61 and =83 cm. Plot this potential, with values for , Re (the value of R at the potential energy minimum), and & indicated on the appropriate axes. Calculate B(T) and AE/E for Ar gas at P=1.0 bar and T=298 K. Explain why these values are positive and/or negative.

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