(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
(a) Show that the entropy change of a Van der Waals gas for an isothermal change...
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...
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...
. Derive an expression for isothermal, reversible expansion for a van der Waals gas. Is the work done on the surroundings more or less compared to an ideal gas?
The van der Waals gas is a useful model of a real gas, and we know the source of the parameters a and b. It is instructive to see how these parameters affect the work done during isothermal reversible expansion. Calculate this work, and account physically for the way that a and b appear in the final expression. For answering the second part, assume that nb is much less than the final and initial volumes. Represent the work done in...
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...
The van der Waals equation of state for a real gas is (P+ ) (V - nb) = nRT At what pressure will 1.00 mole of CH4 be in a 10.0 L container at 298 K assuming CH4 is a real gas. (van der Waals constants for CH4 are α = -2.253 L2 atm mol-2. b = 0.04278 L mol-1) 2.43 atm 2.28 atm 2.51 atm 24.5 atm 0.440 atm
1(a) Show that the entropy of the van der Waals gas is ơ-N{InP0(NNb1 Show that the energy is U 3Nt/2 - N2a/V. (c) Show that the enthalpy H U pV is 5/2). (b) the results are given to first order in the van der Waals correction terms a and b.
12 This question explores the energy transfer during the reversible isothermal expansion of a van-der-Waals gas. a) The equation of state of the van-der-Waals gas is 141 where Vm is the molar volume. Explain the significance of the constants a and b giving a physical interpretation of both by comparing the equation given with the equation of state of the ideal gas. b) Re-arrange the equation of state given above to produce a formula for the pressure [3] as a...
A van der Waals gas undergoes an isothermal reversible compression under conditions such that z=0.95. What is the ratio of the work for this process compared to the work for the same process with an ideal gas?