The van der Waals gas is a useful model of a real gas, and we know...
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 terms of the work done for an ideal gas (Hint: ln(1 + x) ≈ x for x << 1)
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The van der Waals gas is a useful model of a real gas, and we
know...
Problem 3: PV Work for a van der Waals Gas (1 points) The work for a...
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...
. Derive an expression for isothermal, reversible expansion for a van der Waals gas. Is 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?
(a) Show that the entropy change of a Van der Waals gas for an isothermal change...
(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
This question also asks for plots - please remember to include them! Final volume isn't given, ju...
This question also asks for plots - please remember to include
them!
Final volume isn't given, just leave it in the formula as
vf.
Calculate the work done during the isothermal reversible expansion of a Van der Waals gas. Account physically for the way in which the coefficients a and b appear in the final expression. Plot on the same graph the indicator diagrams for the isothermal reversible expansion of (a) a perfect gas, (b) a van der Waals gas...
A van der Waals gas undergoes an isothermal reversible compression under conditions such that z=0.95. What...
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?
12 This question explores the energy transfer during the reversible isothermal expansion of a van-der-Waals gas....
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...
Initially, at a temperature T, and a molar volume vi, a van der Waals gas undergoes...
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...
2. One mole of a monoatomic van der Waals gas obeys the equation of state and its internal energy is expressed as U-Суг...
2. One mole of a monoatomic van der Waals gas obeys the equation of state and its internal energy is expressed as U-Суг_ _ where Cv is the molar isochoric heat capacity of an ideal gas. The gas is initially at pressure p and volume V. (i) Explain the physical meaning of the parameters a and b in the equation of state of the gas (ii) Calculate the heat transferred to the gas during reversible isothermic expansion to the volume...
Determine an expression for for an ideal gas and for a van der Waals gas. Op...
Determine an expression for
for an ideal gas and for a van der Waals gas.
Op 5
The van der Waals equation of state was designed (by Dutch physicist Johannes van der Waals)...
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...
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...
This question also asks for plots - please remember to include
them!
Final volume isn't given, just leave it in the formula as
vf.
Calculate the work done during the isothermal reversible expansion of a Van der Waals gas. Account physically for the way in which the coefficients a and b appear in the final expression. Plot on the same graph the indicator diagrams for the isothermal reversible expansion of (a) a perfect gas, (b) a van der Waals gas...
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...
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...
2. One mole of a monoatomic van der Waals gas obeys the equation of state and its internal energy is expressed as U-Суг_ _ where Cv is the molar isochoric heat capacity of an ideal gas. The gas is initially at pressure p and volume V. (i) Explain the physical meaning of the parameters a and b in the equation of state of the gas (ii) Calculate the heat transferred to the gas during reversible isothermic expansion to the volume...
Determine an expression for
for an ideal gas and for a van der Waals gas.
Op 5
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...
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