# UCI CBEMS 45C - HW2_45C_Sp15 (2 pages)

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## HW2_45C_Sp15

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## HW2_45C_Sp15

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School:
University of California, Irvine
Course:
Cbems 45c - Chem Eng Thermodyns
##### Chem Eng Thermodyns Documents
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CBEMS 45C Chemical Engineering Thermodynamics Spring 2015 Homework 2 Due at the BEGINNING of lecture on 04 17 2015 1 The Clausius equation of state describes the behavior of a certain fluid P V b RT with b 10 5 m3 mol For this fluid CP 25 4 10 2 T J mol K a Derive an explicit algebraic expression for the CP of the fluid valid at any pressure b The pressure of the fluid must be reduced from 4 MPa to 800 kPa The initial temperature of the fluid is 300 K Your colleagues are considering two different ways of reducing the pressure either by passing the fluid through a throttling valve or by passing it through a small gas turbine that runs reversibly and adiabatically What will the final temperature of the fluid be in each case 2 Assume that nitrogen can be described by the virial equation of state B C PV 1 2 RT V V with B 10 5 m3 mol and C 1 5 10 9 m6 mol2 In an industrial process 40 moles of nitrogen is being isothermally compressed at 20 C from 1 bar to 100 bar in a piston and cylinder device Calculate the work required for this compression the amount of heat that must be removed to keep the process isothermal and the amount of entropy generated in the gas during this process 3 Assuming that the van der Waals equation of state is applicable for methane answer the following questions a Calculate H S and U in going from 300 K and 10 MPa to 200 K and 4 MPa and compare your answers to those obtained from Figure 3 3 2 Comment on the accuracy of the van der Waals equation of state b One mole of methane initially at 100 kPa and 300 K is isothermally compressed to 10 MPa Determine the molar volume at the initial and final conditions and the amount of work necessary to carry out the isothermal compression 4 The following data is available from the steam tables for a temperature of 350 C this data will be available on the course website 1 Specific Volume m3 kg 0 0013118 0 0013538 0 001397 0 001442 0 0014894 0 0015405 0 0015975 0 0016657 0 0022098 0 002782 0 0035023 0 0044092 0 0055508 0 0069881 0 010029 0 015953 0 022442 0 030243 0 039859 0 051834 0 066818 0 085617 0 10924 0 13894 0 17630 0 22332 0 28249 0 35698 0 45074 0 56878 0 71737 0 90443 Pressure bar 1000 0 794 33 630 96 501 19 398 11 316 23 251 19 199 53 165 29 165 29 165 29 165 29 165 29 165 29 158 49 125 89 100 00 79 433 63 096 50 119 39 811 31 623 25 119 19 953 15 849 12 589 10 000 7 9433 6 3096 5 0119 3 9811 3 1623 a Using your choice of software e g Excel Matlab Scilab etc plot the above isotherm data on a P V plot P on y axis specific volume on x axis Plot both axes on a log scale b On the same axes plot the corresponding isotherm predicted by the idea gas law c On the same axes plot the corresponding isotherm predicted by the van der Waals equation of state d Comment on the range of accuracy for the two equations of state Notes use the appropriate vdW constants for water and watch units Include a legend and axes labels 2

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