Consider a cylinder with a movable piston containing nn moles of a Van der Waals gas. The entire apparatus is immersed in a constant temperature bath of temperature TT kelvin. The piston pushes slowly outward on an external body that matches the force momentarily at each instant so that the gas expands quasi-statically from a volume V1V1 to V2V2 at constant temperature TT. The isothermal process is shown in the figure, where the pressure pp is related to the volume VV by the Van der Waals equation of state, as follows: (p+a/V2)(V−b)=nRT(p+a/V2)(V−b)=nRT where RR is the ideal gas constant, and aa and bb are empirically determined constants. Part (a) Write an expression for the work WW done by the gas on the external body. W = n R T ln( (V1 - b)/(V2 - b) ) + a ( 1/V1 - 1/V2 ) W = n R T ln( (V2 - b)/(V1 - b) ) + a ( 1/V2 - 1/V1 ) W = n R T ln( (V2 - b)/(V1 - b) ) - a ( 1/V22 - 1/V12 ) W = n R T ln( V1 - V2 ) + a ( 1/V1 - 1/V2 ) W = n R T ln( (V1 - b)/(V2 - b) ) - a ( 1/V12 - 1/V22 ) W = n R T ln( V2 - V1 ) + a ( 1/V2 - 1/V1 ) Part (b) For nnn = 4 moles, TTT = 290 kelvin, V1V1V_1 = 1.7 liters and V2V2V_2 = 3V1V1V_1, determine the work done by the gas on the external body. The gas constant is RRR = 8.314 J K-1 mol-1, aaa = 0.45 joule-liters and bbb = 0

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Problem 7: Consider a cylinder with a movable piston containing nn moles of a Van der Waals gas. The entire apparatus is immersed in a constant temperature bath of temperature TT kelvin. The piston pushes slowly outward on an external body that matches the force momentarily at each instant so that the gas expands quasi-statically from a volume V1V1 to V2V2 at constant temperature TT. The isothermal process is shown in the figure, where the pressure pp is related to the volume VV by the Van der Waals equation of state, as follows:

(p+a/V2)(V−b)=nRT(p+a/V2)(V−b)=nRT

where RR is the ideal gas constant, and aa and bb are empirically determined constants.

Part (a) Write an expression for the work WW done by the gas on the external body.

W = n R T ln( (V₁ - b)/(V₂ - b) ) + a ( 1/V₁ - 1/V₂ )

W = n R T ln( (V₂ - b)/(V₁ - b) ) + a ( 1/V₂ - 1/V₁ )

W = n R T ln( (V₂ - b)/(V₁ - b) ) - a ( 1/V₂² - 1/V₁² )

W = n R T ln( V₁ - V₂ ) + a ( 1/V₁ - 1/V₂ )

W = n R T ln( (V₁ - b)/(V₂ - b) ) - a ( 1/V₁² - 1/V₂² )

W = n R T ln( V₂ - V₁ ) + a ( 1/V₂ - 1/V₁ )

Part (b) For nnn = 4 moles, TTT = 290 kelvin, V1V1V_1 = 1.7 liters and V2V2V_2 = 3V1V1V_1, determine the work done by the gas on the external body. The gas constant is RRR = 8.314 J K-1 mol-1, aaa = 0.45 joule-liters and bbb = 0.

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