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Problem session 2 problems0 - Given that μ =(2a/RT-b/C p,m...

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Chem 3321 Fall, 2009 Problem Session 2 problems 1. The internal energy of a perfect monatomic gas relative to its value at T = 0 is 2 3 nRT. Calculate ( 29 ( 29 T T V H V U and for the gas. 2. The isothermal compressibility of lead is 2.21 x 10 -6 atm -1 . Express this value in Pa -1 . A cube of lead of side 10 cm at 25 C was to be inserted in the keel of an underwater exploration TV camera, and its designers needed to know the stresses in the equipment. Calculate the change of the volume of the cube at a depth of 1.000 km (disregarding the effects of temperature). Take the mean density of sea water as 1.03 g cm -3 . Given that the expansion coefficient of lead is 8.61 x 10 -5 K -1 and that the temperature where the camera operates is –5 C, calculate the volume of the block taking the temperature into account too. 3. A sample consisting of 1.00 mol of a van der Waals gas (see Chapt 7) is compressed from 20.0 L to 10.0 L at 300 K. In the process, 20.2 kJ of work is done on the gas.
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Unformatted text preview: Given that μ = {(2a/RT)-b}/C p,m with C p,m = 38.4 J K-1 mol-1 , a = 3.60 L 2 atm mol-2 , and b = 0.44 L mol-1 , calculate ∆ H for the process. 4. Derive the relation ( 29 ( 29 U T V T V V U C ∂ ∂ ∂ ∂-= from the expression for the total differential of U(T,V). 5. Starting from the expression ( 29 ( 29 P V v p T V T P T C C ∂ ∂ ∂ ∂ =-, use the appropriate relations between partial derivatives to show that ( 29 ( 29 T P v p P V T V T C C ∂ ∂ ∂ ∂-=-2 Evaluate C p-C v for a perfect gas. 6. Derive an expression for the internal pressure of a van der Waals gas (see eqn 7.1) in terms of a, b, and V m . Use the expression to show that μ = {(2a/RT)-b}/C p,m by using the definition of μ and appropriate relations between partial derivatives. (Hint: Use the approximation pV m ≈ RT when it is justifiable to do so.)...
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