Question

The equation of state for a van der Waals fluid is

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(P+4E) (v – NB) = NKT

You will look at the work and energy it takes to compress such a fluid and compare it to an ideal gas.

1. Show that the following identity is true using thermodynamic identity for U and Maxwell’s Relations.

   

2. Using part (a), show that for a van der Waals fluid, the internal energy for a monatomic

   

3. Take a van der Waals fluid at 101 kPa, 300 K, and an initial volume of 1 m3. It is then compressed isothermally to a final volume of 0.5 m3. From N2 gas, the book gives a = 4 × 10−49 Jm3 and b = 6 × 10−29 m3. What is the change in internal energy? Compare this to the change in energy if this were an ideal gas.

Answer 1

consider Internal Energy as function of (T,V).

U= U(T,V)

page du= C dT +/T (OP) Jav - N2 from ea 1 NKT UND uz NK V-Nb 2Т /V NKT TV CU-ND) from vandervaal's con of state the above quantity becomes pt an - NET E TOP NKT Cu-Nb) put as from above eght egh Ô I du= Cudi + (p tan3 p) dv. du= adt & an2 dr. a & for mono atomic gas bet jau a 3RT - aN? V RE KN | U= 3 RT - ON 10 NXT - ON2