452 Midterm 1 2009 - Chemistry 452 Enter answers in a Blue...

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Chemistry 452 July 24, 2009 Enter answers in a Blue Book Midterm Examination Key Useful Constants: 1 Newton=1 N= 1 kg m s -2 1 Joule=1J=1 N m=1 kgm 2 /s 2 1 Pascal=1Pa=1N m -2 1atm=101325 Pa Universal Gas Constant R=8.31 J K -1 mol -1 =0.0821L atm K -1 mol -1 Avagadro’s Number N A =6.024x10 23 mol -1 All answers must be in MKS units (i.e. units of meters, seconds, kilograms, Joules, Pascals etc.) Part 1 (18 points) Answer THREE out of the following SIX questions. Limit definitions to less than 200 words. Use equations where helpful or required, but detailed calculations are not necessary. Question 1.1 . Define Euler’s Criterion for Exactness. Explain how this rule is relevant to the field of thermodynamics. A differential, () ,, M xyd x N xyd y + is exact if there exist a function Z(x,y) such that y x ZZ dZ dx dy M x y dx N x y dy xy ⎛⎞ ∂∂ =+= + ⎜⎟ ⎝⎠ . The criterion for exactness is therefore 2 M NZ yx x y ∂∂∂ == . The path integrals of exact differentials are dependent only on the initial and final states of the path, not on the details of the path itself. Differentials of state functions are exact so when integrated over specific paths, the state function change is dependent only on the definitions of the initial and final states. (74 words) Question 1.2 . The entropy has been defined as “time’s arrow”. Explain this definition using thermodynamic reasoning. Utilize in your argument the statistical interpretation of entropy. The equations of mechanics (F=Ma) are time reversible. This means they are as valid going forward in time as going backwards. In contrast, the entropy of an isolated system increases from initial to final state, or remains the same. The final state is understood to be reach later in time, so moving toward the final state is marked by increased entropy. The reversal of mechanics in an isolated system , which in turn would decrease the entropy is not impossible, but is nevertheless a highly improbable event. (87 words) Question 1.3 What is the Law of Dulong and Petit for an atomic crystal? Explain this law in terms of the mechanical motions of the atoms in the crystal.
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The heat capacity of an atomic crystal approached 3R as the temperature increase. This behavior results because at high temperature a atomic crystal obeys the equipartition theorem, which distributes energy equally among mechanical degrees of freedom. Each atom is a three dimensional oscillator, with two degrees of freedom per dimension, or six in all. The heat capacity is thus expected to be: 6x3R/2=3R, as stated by the Dulong-Petit Law. (69 words) Question 1.4 Explain the concept of reversibility as it applies to thermodynamic pathways. A system is displaced from its initial state by application of an infinitesimal force. The system is allowed to re-equilibrate before further application of the force. Thus the system’s path consists of a sequence of equilibrium states separated by these small displacements and any step can be reversed by application of an infinitesimal force. The equation of state is valid along a reversible path. (64 words).
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This note was uploaded on 10/26/2010 for the course CHEM 452 taught by Professor Khalil during the Summer '08 term at University of Washington.

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452 Midterm 1 2009 - Chemistry 452 Enter answers in a Blue...

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