Must show all work to receive full credit. 1) Derive an equation for the work re

Question

Must show all work to receive full credit.

1) Derive an equation for the work required to perform thefollowing:
      a) Expand an ideal gas reversiblyand isothermally from initial volume Vi to final
volume Vf. (Hint: derive equation 2.11)
      b) Expand a Berthelot gas reversiblyand isothermally from initial volume Vi to final
volume Vf.
      c) Compare what you’ve foundfor a) and b). Describe the differences between the
equations. How do the Berthelot parameters specifically (i.e. whatterms are the
same, which are different) affect the magnitude of the workrequired to expand
the gases?

Explanation / Answer

a) W = integral [P*dV] P = nRT/V          W = integral [nRT*dV/V] = nRT*integral [ dV/V] = nRT*lnV =nRT(lnVf - lnVi) = nRT*ln(Vf/Vi) b) (P + a*n2/TV2)*(V-nb) = nRT P = nRT/(V-nb) - a*n2/TV2 W = nRT* integral [dV/(V-nb)] -(an2/T)*integral[dV/V2] W = nRT*ln(V-nb) + (an2/T)*(1/V)                                           Vf -nb                              1                   1 W = nRT ln ------------     + (an2/T)*{ ------    -     --------}                      Vi -nb                              Vf                  Vi c) The difference is gone when b = a = 0 The reason b is not 0 is that real gases are not point particles;they occupy space. Ideal gases are point particles The reason a is not 0 is that real gases have interactions betweengas particles. Ideal gas particles do not.

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