Work calculation on multiple different steps. Not sure how to do b-d. 5-21 Exerc

Question

Work calculation on multiple different steps. Not sure how to do b-d. 5-21 Exercise 5-6 400,92 moles of nitrogen gas (which may be assumed to behave as an ideal gas) is to be compressed isothermally at 300.0 K from an initial pressure of 1.000 atm to a final pressure of 100.0 atm. Calculate the minimum (no friction) work required for this process if: (a) the extermal pressure is set at 100 atm (i.e., just slightly greater than 100 atm) and the compression is carried out in one fun, fast, and easy step (see the PV-diagrams below), (b) the compression is carried out in two easy steps by first compressing to V,-0.9869 m' using an external pressure of P, throughout, followed by compressing to V, using an external pressure of P, 100+ atm throughout. the compression is carried out in four steps: to V,-3.1209 m'using ;, then to V, 0.9869 m' using P, next to ,-0,31209 m using P, and finally tousing P,-100 am. that are not fun, infinitely slow, and definitely not easy to carry out. (d) the compression is carried out using a very large number of "reversible"or "q uasi-static" steps 1-step 2-steps State 2 Lotsa sepst 4-steps Copyright © 2011 by F.R. Foulkes

Explanation / Answer

2. We can consider nitrogen as ideal gas as itvis given in question

Caluclating initial volume by PV=NRT

P=1 atm

N=400.92

R=8.314

T=300k

We get initial Volume =9.8689m3

Same way we caluclate final volume at p=100 atm

Final volume=0.098689m3

Work done at constant pressure is=p(v1-v2)

Total work done is ={1(9.8689-0.9869)+100(0.9869-0.09869)}*101325

=1799.947KJ

Work done at constant volume is zero.

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