Explanation Consider the van der Waals equation of state. Write the van der Waals equation of state. p = R T v − b − a v 2 Here, universal gas constant is R , the temperature is T , the pressure is p , the specific volume is v , and the van der Waals constants are a , b . Write the differential of a function p = p ( v , T ) . d p = ( ∂ p ∂ T ) v d T + ( ∂ p ∂ v ) T d v d p = M d T + N d v (I) Refer Equation (I). The expression for M is as follows. M = ( ∂ p ∂ T ) v (II) Here ( ∂ p ∂ T ) v is the partial derivative of the p with respect to T at which the variable v being held constant. Substitute ( R T v − b − a v 2 ) for p in Equation (II). M = ∂ ∂ T ( R T v − b − a v 2 ) Partial differentiate with respect to temperature. M = R v − b − 0 M = R v − b Refer Equation (I). The expression for N is as follows. N = ( ∂ p d v ) T (III) Here ( ∂ p d v ) T is the partial derivative of the p with respect to v at which the variable T being held constant

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118412930

Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

Publisher: WILEY

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Chapter 11.9, Problem 35CU

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Indicate the following statement is true or false.

The following expression is the differential of an equation of state p=p(v,T)dp=(−Rv−b)dT+(−RT(v−b)2+2av3)dv.

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Chapter 11.9, Problem 34CU

Chapter 11.9, Problem 36CU

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Indicate the following statement is true or false. The following expression is the differential of an equation of state p = p ( v , T ) d p = ( − R v − b ) d T + ( − R T ( v − b ) 2 + 2 a v 3 ) d v .

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Indicate the following statement is true or false. The following expression is the differential of an equation of state p=p(v,T)dp=(−Rv−b)dT+(−RT(v−b)2+2av3)dv.

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Chapter 11 Solutions

Indicate the following statement is true or false.

The following expression is the differential of an equation of state p=p(v,T)dp=(−Rv−b)dT+(−RT(v−b)2+2av3)dv.