Chemistry 5302 Homework Problem Set 1 McQuarrie, Chapters 1 and 2 1. McQuarrie, Problem 1-29: Use the thermodynamic square to derive the equation of state: ∂E ∂p −T = −p (1) ∂V N,T ∂T N,V 2. Use the canonical ensemble partition function to derive the equation of state: ∂p ∂E +β = −p ∂V N,β ∂β N,V (2) 3. McQuarrie, Problem 2-1: Use the equivalence of the equations of state in (1) and (2) to show that: 1 (3) β∝ T Why can’t β = constant × T ? 4. Equating the statistical mechanical energy E with the thermodynamic internal energy E, show that E can be written: ∂ ln Q 2 E = kT (4) ∂T N,V 1
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