Please show all steps to the problem Thank You! Moles of ideal gas at 300 K at a

Question

Please show all steps to the problem

Thank You!

Moles of ideal gas at 300 K at an initial pressure of 10 atm are expanded iso thermally to a final pressure of 5 atm in 49 stages. In stage 1 the gas. initially at 10 atm, is expanded against a constant pressure of 9.9 atm. In stage 2 the gas. initially at 9.9 atm. is expanded against a constant pressure of 9.8 atm. In stage 3 the gas, initially at 9.8 atm, is expanded against a constant pressure of 9.7 atm. etc. Eventually, in the last stage stage (the 49th stage), the gas. initially at a pressure of 5.1 atm is expanded against a constant pressure of 5 atm. Calculate W for the total 49-step process. How close is this to the maximum W performed in a reversible isothermal expansion from 10 atm to 5 atm?

Explanation / Answer

Given

Initial pressure                  P = 10 atm

Final pressure                    P’ = 5 atm

Temperature                     T = 300 K

Number of moles            n = 5 mol

Universal Gas constant R = 0.08205 L atm / mol·K

Solution

Finding initial volume

PV =nRT

10V = 5 x 0.08205 x 300

V = 12.3075 L

Final volume

P’V’ = nRT

5V’ = 5 x 0.08205 x 300

V’ = 24.615 L

Work done in isothermal process

W = RT.ln(V’/V)

R in SI units is 8.314 J / (mol·K)

W = 8.314 x 300 x ln(24.615/12.3075)

W = 1728.85 J

W = 1.73 kJ

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