CBEMS 45C Chemical Engineering Thermodynamics, Spring 2015Homework 2Due at the BEGINNING of lecture on 04/17/20151. The Clausius equation of state describes the behavior of a certain fluid:P (V − b) = RTwith b = 10−5m3/mol. For this fluid, C∗P= 25 + 4 × 10−2T J/(mol K)(a) Derive an explicit algebraic expression for the CPof 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 thefluid is 300 K. Your colleagues are considering two different ways of reducing the pressure; eitherby passing the fluid through a throttling valve, or by passing it through a small gas turbine thatruns 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:P VRT= 1 +BV+CV2with B = −10−5m3/mol and C = 1.5× 10−9m6/ mol2. In an industrial process, 40 moles of nitrogen isbeing isothermally compressed at 20◦C from 1 bar to 100 bar in a piston and cylinder device. Calculatethe work required for this compression, the amount of heat that must be removed to keep the processisothermal, 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 followingquestions:(a) Calculate ∆H, ∆S, and ∆U in going from 300 K and 10 MPa to 200 K and 4 MPa, and compareyour answers to those obtained from Figure 3.3-2. Comment on the accuracy of the van der Waalsequation 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 necessaryto carry out the isothermal compression.4. The following data is available from the steam tables for a temperature of 350◦C (this data will beavailable on the course website):1Specific Volume (m3/kg) Pressure (bar)0.0013118 1000.00.0013538 794.330.001397 630.960.001442 501.190.0014894 398.110.0015405 316.230.0015975 251.190.0016657 199.530.0022098 165.290.002782 165.290.0035023 165.290.0044092 165.290.0055508 165.290.0069881 165.290.010029 158.490.015953 125.890.022442 100.000.030243 79.4330.039859 63.0960.051834 50.1190.066818 39.8110.085617 31.6230.10924 25.1190.13894 19.9530.17630 15.8490.22332 12.5890.28249 10.0000.35698 7.94330.45074 6.30960.56878 5.01190.71737 3.98110.90443 3.1623(a) Using your choice of software (e.g., Excel, Matlab, Scilab, etc.), plot the above isotherm data ona 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 ofstate.(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