1. The Dieterici equation of state for a gas is kBT where u = V/N. Find the critical point and compute the ratio Pete/kaTe Calculate the critical exponents β, δ, and γ. 1. The Dieterici equa...
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.
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...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds-
1 point)...
4. (1 pt) Calculate Tu, T, and n(u, v) for the parametrized surface at the given point Then find the equation of the tangent plane to the surface at that point Ф(и, у) %3D (2и + v, и — 4v, 5и); Ти The tangent plane: V u=4, v6 , n(u,v) TV =9z
(a) One mole of a monoatomic van der Waals gas obeys the equation of state A3. ) (V-b)=RT (p+ and its internal energy is expressed as U CvT 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) Write down the equation that defines entropy in thermodynamics. Define...
1. The Redlich-Kwong equation of state is given by P=_RT___ A _ _ V-RI2,, - 0.0866 - where 4-0.42748RT - B - P (The R-K constants can be calculated from the critical temperature and pressure of the gas.) This EOS was introduced in 1949 and is adequate for calculations of gas phase properties when P, </2 T, a) Derive an expression for the work associated with an isothermal reversible volume change of a R-K gas between two volumes V, and...
deal gases obey the equation PV nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of gas, T is its temperature, and the constant R-8.314 KPa-liters-mol-1 kelvin-1 (a) Find the exac t change in volume of O, gas as the pressure increases from 12.00 to 12.01 KPa, the temperature decreases from 300.0 to 299.9 degrees kelvin, and the number of moles of 0, gas changes from 1.03 to 1.01 moles....
TSD.1 In this problem, we will see (in outline) how we can calculate the multiplicity of a monatomic ideal gas This derivation involves concepts presented in chapter 17 Note that the task is to count the number of microstates that are compatible with a given gas macrostate, which we describe by specifying the gas's total energy u (within a tiny range of width dlu), the gas's volume V and the num- ber of molecules N in the gas. We will...