Chemistry 350 . .. Winter 2011 Problem Set # 1 R.J. Le Roy Due: Monday, January 24 Submit STAPLED Solutions in Class or to my oﬃce (ESC-332) by 5:00 PM 1. Evaluate the ﬁrst derivative with respect to x of each of the functions: a) sin(3 x ) e 2 x 2 b) cos (3 x ) e 2 x-e-2 x c) (7 x 2 + 3 /x ) π d) [ sin(3 x ) ] 2 x 2. We will see later in the course that the equation of state of a substance (the expression which interrelates allowed values of the macroscopic variables P , V , T and N ) and the thermodynamic internal energy U are related to the “total system partition function” Q by the expressions: P = k B T ± ∂ ln Q ∂V ² N,T and U = k B T 2 ± ∂ ln Q ∂T ² N,V where k B is Boltzmann’s constant. Assuming the following expression for the total partition function for an N-particle sample of a gas of atoms of mass m at temperature T and volume V : Q ( N,V,T ) = 1 N ! ± 2 π mk B T h 2 ² 3 N/ 2 [ V-Nb ] N e aN 2 /V k B T in which a and b are constants characterizing the gas and h is Planck’s constant. (a) Using the above equation for
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This note was uploaded on 09/28/2011 for the course CHEM 350 taught by Professor Prof.djasd during the Winter '10 term at Waterloo.