The Dieterici equation of state is similar to the van der Waals equation in that theyboth employ gas-specific constants a and b to attempt to account for the interaction betweenmolecules and the nonzero volume of the individual molecules of gas. However, the Dietericiequation of state has a significantly different functional form:P(V – b) = RTe-a/(rVT)Note that a and b are constants (n is implicitly constant as volume is expressed as molarvolume).What are the following partial derivatives for the Diererici equation of state?ӘРa)b)ƏP.T

For partial derivative variables other than with respect to which derivative is being taken are…

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Part A: 10 moles of ideal gas initially at 10 atm and 250 K is expanded isothermally and reversibly to a final pressure of 2 atm. Calculate W, AU, and Q in Joules. Part B: The same gas in problem A, starting in the same initial state, is expanded isothermally against a constant external pressure of 2 atm, to a final pressure of 2 atm. Calculate W, AU, and Q in Joules for this irreversible process. Part C: The same gas in part B, starting in the same initial state, is expanded isothermally to a final pressure of 2 atm. The process is carried out in 4 stages. First the gas is expanded against a constant pressure of 8 atm, to 8 atm. Then the gas is expanded against a constant pressure of 6 atm, to 6 atm. Then the gas is expanded against a constant pressure of 4 atm, to 4 atm. Finally, the gas is expanded against a constant pressure of 2 atm, to 2 atm. Calculate W, AU, and Q in Joules for the 4-step process.
Derive the thermodynamic equation of state from the fundamental equation for enthalpy (OT), ән (OH!) T =V-T HINT: you will need to use a Maxwell relation. Derive an expression for an ideal and (b) a van der Waals gas. ән Әр T for (a)
A container is filled with an ideal diatomic gas to a pressure and volume of P1 and V1, respectively. The gas is then warmed in a two-step process that increases the pressure by a factor of two and the volume by a factor of three. Determine the amount of energy transferred to the gas by heat if the first step is carried out at constant volume and the second step at constant pressure. (Use any variable or symbol stated above as necessary.)
A container encloses 2 mol of an ideal gas that has molar mass M₁ and 0.5 mol of a second ideal gas that has molar mass M2 = 3M₁. What fraction of the total pressure on the container wall is attributable to the second gas? Note: The kinetic theory explanation of pressure leads to the experimentally discovered law of partial pressures for a mixture of gases that do not react chemically: The total pressure exerted by the mixture is equal to the sum of the pressures that the several gases would exert separately if each were to occupy the vessel alone.
4. when the tempeakue of a gas is will begin do metice departures fiom reduced the ideal chacactenaed you law. These departeres are gud by the Van den Waals equatron of fhen stake V-6 RT when V= Y is the woleume per mole, and a and b ari the Table a(Nm") " Von der Waals cmstenta" Van den Weals consdunts b (m3) 2.38X105 2.65X10 He 3.46 X103 2.47x162 1. 34 x107 1.38x101 Itz -5 -5 3.87 xi0 Nz Oz 3.18X10 1
Interstellar space is quite different from the gaseous environments we commonly encounter on Earth. For instance, a typical density of the medium is about 1 atom cm−3 and that atom is typically H; the effective temperature due to stellar background radiation is about 10 kK. Estimate the diffusion coefficient and thermal conductivity of H under these conditions. Compare your answers with the values for gases under typical terrestrial conditions. Comment: Energy is in fact transferred much more effectively by radiation.
Using the same procedure to determine the fundamental equation of chemical thermodynamics (dG = –SdT + VdP) from the Gibbs free energy of a system (G = H – TS), can you please explain how to find the analogous fundamental equation for (A=U-TS)? Also, can you please handwrite the formula down instead of typing? I get confused with typed formulas sometime.
The gas law for a fixed mass mm of an ideal gas at absolute temperature T, pressure P, and volume V is PV=mRT, where R is the gas constant. Find the partial derivative (∂P/∂V) (∂V/∂T) (∂T/∂P) = ?
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