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Equation of the gas state processes

Problem 2.22

One mole of nitrogen is contained in a vessel of volume VV =1.00=1.00 l. Find: (a) the temperature of the nitrogen at which the pressure can be calculated from an ideal gas law with an error η=10%\eta=10 \% (as compared with the pressure calculated from the Van der Waals equation of state); (b) the gas pressure at this temperature.

Reveal Answer
 (a) T=a(V−b)(1+η)/RV(ηV+b)=133 K;(b)p=RT/(V−b)−a/V2=9.9extatm.\text { (a) } T=a(V-b)(1+\eta) / R V(\eta V+b)=133 \quad \mathrm{~K} ; \text {(b)} p=R T /(V-b)-a / V^{2}=9.9 ext { atm. }
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