Need problem 8 help, Can you explain why you do something and show all steps ple

Question

Need problem 8 help, Can you explain why you do something and show all steps please. Thank you.

8. The turbo-alternator in a coal-burning power plant generates A.C. electricity by rotating a bundle of wires through a magnetic field. The torque is provided by a turbine which itself is powered by steam generated by burning coal. Let^?s say that the turbine initially has no volume but is suddenly filled with a constant external pressure of steam (100 atm) that moves a 1 0 m^2 piston 10 m in length. How much work does this take? (5 pts)

Explanation / Answer

a. The Berthelot equation of state has cosntants a and b

The untis of a = m^6.Pa/mol

and,

the units of b = m^3/mol

the equations for,

a = 27R^2Tc^2/64Pc

and,

b = RTc/8Pc

where,

R = gas constant in m^3.Pa/K.mol

Tc = Temperature in K

Pc = pressure in Pa

Feed units of each in equations of a and b,

a = (27/64)(m^3.Pa/K.mol)^2(K)^2/Pa

   = (27/64)(m^6.Pa^2/K^2.mol^2.Pa)

   = (27/64)(m^6.Pa/mol^2) units

For b,

b = m^3.Pa.K/8.K.mol.Pa

   = (1/8)m^3/mol units

5. b will be 0.003 m^3/mol for the equation given here.

6. the values of residual volume would be negative for the compressibilty factor of 1.

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