Question

physical chemistry

3. Derive formulas for AE, Aw, and Aq when a Van der Waal's gas undergoes: a) reversible isothermal expansion b) adiabatic expansion c) repeat steps a and b for an ideal gas d) Use the Maxwell relation derived from the Helmholtz free energy F =F(T,V) = -SdT PdV To prove that e) Determine for a Van der Waal's gas and an ideal gas. T()-P f) Explain the answer to part e in terms of the assumptions that define VdW's and ideal gases g) Explain the difference between the answers to parts a and b vs part c. How does the difference in (for VdW's and ideal gases affect the energy, heat, and work change of isothermal and adiabatic expansion?

Answer 1

Multiple sub-parts as per guideline only first 4 sub-parts will be answered :

3. (a) reversible isothermal expansion for real gas

(b) adiabatic exapnsion for Vander waal gas

(c) a & b for ideal gas

3(9) Reversible isothermal expansion? vander wael's gas equation (Pt 9 (verb) = RT (for are nole work (w) in seversible expension, sw=-1 ep av putting value for 1p) : DE, we have ou y = T ( 22 ) - P for wonder waal equation, since luttnal energy'u can be written El dEa a av an integrating, van 39 sq = DE- W = RT en una SE- W = 6

(b) Adiabatic expansion .sa=0 cadiabatic state) so DE FOW We have, aua ou o at + ( 2 ) av au a ev att a av (from 31a)) an integrating Replacing du wity & E - lauad El dE2 Cuart av an integrating SHE = Soudt + 5 9 av DES GOT + (- 9 - 1 (c) (a) f(b) for ideal gas. Reversible isothermal expansian swang av and RI av A Wa - OV 2 OV CPV2 URT) дws - hвт 142) owa - MRT en

SE=0 since reversible isothermal expansion of ideal gas (DE of Ideal depends on temperature anly, ST2O => DE=o) De =-ow (obat AW 2DE) 10 a = nRT en (U2) 1 Adiabatic expauslan sa=0 Cadiabatic expansion) . DEN OW (adiabatic) we nque aua laudat & W, av du = Cu dT (for ideal gasto or d E- Cu AT IDEA CUATI =o) 1 DECAT a owl or low-fata de

(d) we have , dE = TdS -PdV

on dividing it with dV and applying condition of constant temperature,

we get,

(dE / dV )_T = T (dS/dV)_T - P ...........................i

we have, F(T,V) = -SdT -PdV

using maxwell relation from this,

(dS/dV)_T = (dP/dT)_{v ................................}ii

From i and ii, we get

(dE / dV )_T = T (dP/dT)_v - P