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- 3. In a strictly steady state situation, both the ions and the electrons will follow the Boltzmann relation ( n; = n, exp(- qjø. ). Take Z=1, and calculate plasma kT electrostatic field.Calculate AS (for the system) when the state of 2.00 mol diatomic perfect gas molecules, for which Cp,m = (7/2)R, is changed from 25 C and 1.50 atm to 135 C and 7.00 atm.Consider a system consisting of two oppositely chargedspheres hanging by strings and separated by a distance r1,as shown in the accompanying illustration. Suppose theyare separated to a larger distance r2, by moving them apart.(a) What change, if any, has occurred in the potential energyof the system? (b) What effect, if any, does this process haveon the value of ΔE? (c) What can you say about q and w forthis process?
- (2) The Gibbs function G is (GF) ₁ P == ound ·S (06), = relationship (25) a = -(=++) ₂ thu modynamic property. If =V, prove the following2. Consider a system with 1000 particles that can only have two energies, &, and ɛ, with E, > E,. The difference between these two values is Aɛ = ɛ, - & . Assume that gi = g2 = 1. Using the equation for the Boltzmann distribution graph the number of particles, ni and n2, in states &, and ɛ, as a function of temperature for a A6 = 1×10-21 J and for a temperature range from 2 to 300 K. (Note: kµ = 1.380×10 23 J K-!. " - & % n or = e n, 8,For this problem, use the "Thermodynamic Properties of Selected Substances" table in the "Reference Data" section at the back of your textbook. Suppose you have a mole of methane (CH., otherwise known as "natural gas") at 25°C and atmospheric pressure. (a) rotational, with vibrational frozen out). Further suppose we choose the reference point for the thermodynamic potentials such that we neglect the rest energies of the molecules, and express U as simply 3NRT. Calculate S, H, F, and G for the mole of methane. Suppose the methane behaves as an ideal gas with 6 degrees of freedom (3 translational + 3 If you raise the temperature of the mole of methane to 28°C (keeping the pressure constant), (b) what is the change in its Gibbs free energy? When methane is burned as fuel, the following chemical reaction takes place: CH, + 20, - 2H;0 + CO, (c) Determine the values of AG and AH for this reaction. (d) How much heat is produced in this reaction, per mole of methane?
- Suppose that there is four identical and distinguish particles and should to be placed in four energy levels. E = i x ɛ, i = 0,1,2,3 If we can arrange particles so that the total energy U = 6ɛ. a- find the five macroscopic states and arrange them by the microscopic states. b- prove that the number of the total microscopic states is 44 c- prove that the average population for four quantities is 1.09, 1.09 , 0.91 , 0.917) Use the Maxwell relations to show that the entropy of a perfect gas depends on the volume as Soc R Inv.A sample of Ar of mass 8.30 g occupies 1.75dm3 at 330 K. (a) Calculate the work done when the gas expands isothermally against a constant external pressure of 1 bar until itsvolume has increased by 0.35 dm3 (b) Calculate the work that would be done if thesame expansion occurred reversibly
- At temperature T, the internal energy of 1mol rigid diatomic molecules is =......The fugacity of a monatomic gas is found to obey the relation ?(?, ?) = ????. Write expressions for the molar heat capacity at constant pressure.Show that = Cp – P ƏT. What can be said about (), for an ideal gas and what does this expression represent?