1(a) Show that the entropy of the van der Waals gas is ơ-N{InP0(NNb1 Show that the...
(30pts) Derive expressions for a gas that obeys the Van der Waals equation of state of (P+a⁄v²)(v-b)=RT where v is specific volume and a and b are constants. For an isothermal process derive expressions to calculate change in enthalpy (h), change in internal energy(u), change in entropy (s),
Example 4.6 The fugacity of a van der Waals gas Using the expression for the compressibility factor Z of a van der Waals gas given in equa- tion 1.26, what is the expression for fugacity of a van der Waals gas? As an approximation, terms in P2 and higher in the series expansion are omitted 2-1-0-(0)0r P RT RT Z In P dP P C'P 1 dP RTRT a b P a b RT RT 1Forfe-r a f P exp...
(a) Show that the entropy change of a Van der Waals gas for an isothermal change V1 to V2 is: ΔS = nR ln (V2 - nb / V1 - nb) (b) Calculate ΔS for expanding on mole of NH3 from 2 dm3 to 20 dm3. Compare this to the ideal gas result. b = 0.0371 dm3/mol
4. 10 points A monoatomic gas obeys the van der Waals equation: N²a P= NT V - Nb V2 where N is the number of particles and a and b are known constants and t = kbT. The gas has a heat capacity Cy = 3N/2 in the limit V +0. a) Using the thermodynamic identities and the equation of state prove that acv = 0. av т (3 pts) b) Use the result of part a) to determine the...
The equation of state for a van der Waals fluid is
?
You will look at the work and energy it takes to compress such a
fluid and compare it to an ideal gas.
Show that the following identity is true using thermodynamic
identity for U and Maxwell’s Relations.
Using part (a), show that for a van der Waals fluid, the
internal energy for a monatomic
Take a van der Waals fluid at 101 kPa, 300 K, and an initial...
Problem 3: PV Work for a van der Waals Gas (1 points) The work for a reversible, isothermal expansion of an ideal gas was found by starting with the expression for reversible work --CP V2 P dV V1 and substituting the ideal gas equation of state for P(V,T), to obtain V2 w = nRT ln VI Find an expression for the work of a reversible, isothermal expansion of a van der Waals gas by starting with the same expression for...
Initially, at a temperature T, and a molar volume vi, a van der Waals gas undergoes a change of state to the final temperature T2 and the molar volume V2. The van der Waals gas is characterized by the two parameters a and b (cf. Eq. (3.3)). a. Show that the change in molar entropy is As = c, In 72 + R In º2 = (3.62) 01 - 6 b. A volume of 1 dm is partitioned by a...
• Find the entropy s(u, v) for the Van der Waals Fluid. • Find the equation of adiabats in the Tv plane.
The van der Waals equation of state was designed (by Dutch physicist Johannes van der Waals) to predict the relationship between press temperature T for gases better than the Ideal Gas Law does: b) - RT The van der Waals equation of state. R stands for the gas constant and n for moles of gas The parameters a and b must be determined for each gas from experimental data. Use the van der Waals equation to answer the questions in...
b) Calculate Cp for a van der Waals gas in terms of V,T, and Gy.