2. Derive an expression for (as) for a gas with the equation of state: P(V-nB) = nRT, where B is a constant. 2. De...
Van der Waals equation of state is (P+(n2a)/V2)(V-nb)=nRT where a and b are temperature-independent parameters that have different values for each gas. For CO2, a=0.3640 Pa m6/mol2 and b=4.267*10-5 m3/mol a) Write this equation as a cubic equation in V
3. A gas obeys the equation of state PV = nRT - an'/V, where n is the number of moles of gas and a is constant. Substitute with rearrangement into the differential equation for work, and integrate from Vito V2 to find an equation for the work done by this gas as the result of a reversible isothermal process. Show algebraically that the work is proportional to n to the first power.
3. A gas obeys the equation of state PV = nRT - an'/V, where n is the number of moles of gas and a is constant. Substitute with rearrangement into the differential equation for work, and integrate from Vito V2 to find an equation for the work done by this gas as the result of a reversible isothermal process. Show algebraically that the work is proportional to n to the first power.
10. A nonideal gas obeys the equation of state PV = nRT - api where a is a positive constant. Obtain an expression for the Joule-Thomson coefficient for this gas in terms of the constant a and the heat capacity of the gas. Does the temperature of the gas increase or decrease in a Joule-Thomson experiment? Coorry?
8. 10 Point Bonus! The Ideal Gas Equation of State is pV = nRT, where n= number of moles of gas & R is the ideal the gas constant. The Van der Waals Equation of State is briefly discussed in Ch. 5 of the book by Reif. It is an empirical, crude attempt to improve on the Ideal Gas Model by allowing gas molecules to interact with each other. For one mole of non-ideal gas this equation of state is...
For a Van der Waals gas, the following equations hold. P = nRT/(V−nb) − a(n/V)2 dU = CV dT + a(n/V)2 dV For chlorine gas, CV,m = 25.6 J K−1 mol−1, a = 6.343 bar L2 mol−2, and b = 0.0542 L mol−1. Calculate q, w, ΔU, and ΔH, in joules, when one mole of chlorine gas is expanded isothermally and reversibly at 449 K from 7.0 L to 15.0 L.
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
The van der Waals Equation for real gases is shown below. (P+ ) (v – nb) = nRT In the equation, what assumption we made in the formulation of the Kinetic Molecular Theory of gases for the material-specific constant "a" correct for? O Particle collisions are elastic, so total kinetic energy is conserved The diffusion rate of molecules is indirectly proportional of their molecular weight Gas particles are in constant, random motion Particle volume is negligible
Suppose the parameter b (p= RT/V-b )is temperature dependent. Derive an expression for Cp-Cv forthe equation of state: p=RT/ V-b[T] (assume that the temperature dependence in b is weak and linear in T, i.e b[T] = b0 +b1T)
Write the steps otherwise points will be reduced. (1) Let P=nRT V-nb Find the following: a) b)