E115_Problem_Set_9

E115_Problem_Set_9 - Having estimated the temperature...

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e 115 Engineering Thermodynamics Fall 2009 University of California Problem set 9 Due: Friday, September 25 th , in lecture 1. (15 points) One mole of copper is initially at a temperature of 700K and at a pressure of one atmosphere in a thermally insulated jacket. The system is compressed reversibly to a pressure of 5,000 atmospheres. Compute the change in temperature for this reversible adiabatic process. ( Note : As a simplifying approximation you may treat the molar volume ( 7.11 cm 3 / mol ), the molar constant pressure heat capacity ( 27.0 J/mol K ), and the isobaric volumetric thermal expansion coefficient α = 1 V V T ( ) P = 49. 3 × 10 6 K 1 as constant in this process.)
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Unformatted text preview: Having estimated the temperature change (with the approximation that the molar volume remains constant), now estimate the net expansion (or compression) of the copper as a result of the change of state; normalize the volume change by the molar volume so that you obtain a fractional change. ( Note : Please assume an isothermal compressibility of 0. 735 × 10 − 6 atm − 1 . For simplicity, assume also that this value is independent of pressure and temperature.) 2. (15 points) Derive the Maxwell relationship ∂ T ∂ P ( ) S = ∂ V ∂ S ( ) P from ∂ T ∂ V ( ) S = − ∂ P ∂ S ( ) V ....
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