Consider 1 mole of a van der Waals gas. (i) Derive the expressions for the pressure, pc, temperature, Tc, and volume, Vc, in the critical point of a van der Waals gas in terms of parameters a, b and R. Derive the vdw equation in reduced coordinates p =,= 7, V = V/ (ii) (iii) Find how many times the gas temperature exceeds its critical temperature if the gas pressure is 4 times as high as critical pressure and the volume of gas is equal to twice the critical volume.

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Consider 1 mole of a van der Waals gas.
(i)
Derive the expressions for the pressure, pc, temperature, Tc, and volume, Vc, in the critical
point of a van der Waals gas in terms of parameters a, b and R.
Derive the vdw equation in reduced coordinates p =,= 7, V = V/
(ii)
(iii)
Find how many times the gas temperature exceeds its critical temperature if the gas
pressure is 4 times as high as critical pressure and the volume of gas is equal to twice the
critical volume.
Transcribed Image Text:Consider 1 mole of a van der Waals gas. (i) Derive the expressions for the pressure, pc, temperature, Tc, and volume, Vc, in the critical point of a van der Waals gas in terms of parameters a, b and R. Derive the vdw equation in reduced coordinates p =,= 7, V = V/ (ii) (iii) Find how many times the gas temperature exceeds its critical temperature if the gas pressure is 4 times as high as critical pressure and the volume of gas is equal to twice the critical volume.
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