Assignment 7 Solution

# Assignment 7 Solution - Work done on a van der Waals gas...

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Unformatted text preview: Work done on a van der Waals gas. The equation of state for this gas is parenleftbigg p + a v 2 parenrightbigg ( v- b ) = RT For an isochoric process, W = 0 as there is no volume change. For an isobaric process W = integraltext pdv = p Δ V as the pressure is constant. For an isothermal process we note, p + a v 2 = RT v- b p = RT v- b- a v 2 . Therefore the work done is W = integraldisplay 2 1 pdv = RT integraldisplay 2 1 dv v- b- a integraldisplay 2 1 dv v 2 . Finally, one finds, W = RT ln v 2- b v 1- b + a parenleftbigg 1 v 2- 1 v 1 parenrightbigg . Analysis of the Diesel engine cycle . Constant pressure segment. W 12 = p 1 ( V 2- V 1 ) . Δ U 12 = C V ( T 2- T 1 ) ideal gas . Q 12 = C p ( T 2- T 1 ) . Δ S 12 = integraldisplay 2 1 dQ T = integraldisplay 2 1 C p dT T = C p ln T 2 T 1 . For the adiabatic process: W 23 = integraldisplay 3 2 ( p 2 V γ 2 ) dV V γ = p 2 V γ 2 1- γ parenleftBigg 1 V γ- 1 3- 1 V γ- 1 2 parenrightBigg ....
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Assignment 7 Solution - Work done on a van der Waals gas...

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