# 8.11. The van der Waals equation of state can be written as P kTp/(1 bp) ap,where ρN/V and a and b are positive constants.(e) Find the change in molar internal energy, ae, upon lsothermal expansion(b) Is this change greater or less than that for an adiabatic expansion between theof such a fluid from molar volume v1 to U2,same two volumes?

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This problem is (8.11) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"

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Step 1

Part (a)

For van der Waals equation of states, the equation used for internal energy, E is written below. Divide this equation by N to get an equation for molar internal energy as:

Step 2

Now, for isothermal expansion from molar volume v1 to v2, change in the molar internal energy becomes:

Step 3

Part (b)

For an adiabatic expansion, Q=0. Thus, from first law of thermodynamics,

dE = dQ + dW

dE = 0 – PdV

In this equation, substitute the v...

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