Determine the second virial coefficient B(T) using the van der Waals EOS. Also find its value...
Determine the second virial coefficient B(T) using the van der Waals EOS. Also find its value at the critical temperature where the experimentally observed value is about −0.34 RTc/Pc.
Homework Answers
Second virial coefficient 
Form the virial equation
Residual volume 
From the Vander waals equation of state
Multiply the Vander waals equation by 
Taking limit for 
Where Pv = RT
Therefore 
So a, b constant values
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Determine the second virial coefficient B(T) using the van der Waals EOS. Also find its value...
Example 4.6 The fugacity of a van der Waals gas Using the expression for the compressibility factor Z of a van der Waal...
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...
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...
The van der Waals equation of state was designed (by Dutch physicist Johannes van der Waals) to predict the relationship between pressure p
The van der Waals equation of state was designed (by Dutch physicist Johannes van der Waals) to predict the relationship between pressure p, volume V and temperature T for gases better than the Ideal Gas Law does: 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 the table...
Two moles of a van der Waals fluid are maintained at a temperature T = 0.95TC...
Two moles of a van der Waals fluid are maintained at a temperature T = 0.95TC in a volume of 200cm3. At this temperature, the reduced molar volume of the liquid phase νl ~ 0.68 and that of the gas phase νg ~ 1.7. Assuming the substance to be oxygen (i.e., using the van der Waals constants for oxygen a = 0.138 Pa-m6 and b = 32.6x10-6m3), find the mole number and volume of each phase.
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...
Consider a 50.0 g sample of CO2 in a 150 cm3 vessel at 373 K. Calculate the pressure of the sample using each of the fol...
Consider a 50.0 g sample of CO2 in a 150 cm3 vessel at 373 K. Calculate the pressure of the sample using each of the following approaches: assuming perfect gas behavior (i.e, using the ideal gas law). using the virial equation. The second virial coefficient for CO2 at this temperature is B = -72.2 cm3/mol. [source: Atkins Phys. Chem, 11th ed.] assuming the behavior is described by the van der Waals equation of state, with a = 3.610 atm dm6...
4. 10 points A monoatomic gas obeys the van der Waals equation: N²a P= NT V...
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...
For O2, the van der Waals coefficients a and b are 1.38 L² bar mol-2 and...
For O2, the van der Waals coefficients a and b are 1.38 L² bar mol-2 and 0.0319 L mol-1 respectively. At what temperature will methane act most like an ideal gas? This temperature is called the Boyle temperature. Express your answer to three significant figures and include the appropriate units. H uÅ O 2 ? T = Value Units
Atomic gas which obeys Van der Waals equation of state RT= (P+ a/ V2) (V-b) has...
Atomic gas which obeys Van der Waals equation of state RT= (P+ a/ V2) (V-b) has internal energy (per mole) of u = 3/2 RT - a/V where 'V' is volume of mole in temperature T. In the beginning, the gas temperature is T1 and volume V1. The gas is let to expand adiabatically so that its final volume is V2. What is the final temperature of the gas?
2. (15 marks) The van der Waals equation (first introduced by van der Waals in 1877) is an attemp...
2. (15 marks) The van der Waals equation (first introduced by van der Waals in 1877) is an attempt to describe the fact that real gases do not follow the ideal gas law. According to this equation where P is the pressure of the gas, V is the volume, R is the gas constant, T is the temperature, n is the number of moles, and a and b are parameters that depend on the gas (a) Suppose that 1.0 ±...
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...
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...
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...
For O2, the van der Waals coefficients a and b are 1.38 L² bar mol-2 and 0.0319 L mol-1 respectively. At what temperature will methane act most like an ideal gas? This temperature is called the Boyle temperature. Express your answer to three significant figures and include the appropriate units. H uÅ O 2 ? T = Value Units
2. (15 marks) The van der Waals equation (first introduced by van der Waals in 1877) is an attempt to describe the fact that real gases do not follow the ideal gas law. According to this equation where P is the pressure of the gas, V is the volume, R is the gas constant, T is the temperature, n is the number of moles, and a and b are parameters that depend on the gas (a) Suppose that 1.0 ±...
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