Find the change in entropy of a monoatomic Van der Waals gas using the equation of state nRT an² an² P = and U = nRT V-nb V2 V (Hint: Start from AU = TAS-pdV)
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- Two moles of a monatomic ideal gas such as oxygen is compressed adiabatically and reversibly from a state (3 atm, 5 L) to a state with a pressure of 4 atm. (a) Find the volume and temperature of the final state. (b) Find the temperature of the initial state. (c) Find work done by the gas in the process. (d) Find the change in internal energy in the process. Assume Cv=5R and Cp=Cv+R for the diatomic ideal gas in the conditions given.A monatomic ideal gas undergoes a quasi-static process that is described by the function pV=p1+3(vv1) , where the stating state is (p1,v1) and the final state (p2,v2) . Assume the system consists of n moles of the gas in a container that can exchange heat with the environment and whose volume can change freely. (a) Evaluate the work done by the gas during the change in the state. (b) Find the change in internal energy of the gas. (c) Find the heat input to the gas during the change. (d) What ale initial and final temperatures?For one component gas that is confined in a box with volume V. We can get the entropy of the gas as S= Nk, in- where N is the total a² number of atoms, a is the radius of the atom. Can you guess how it is obtained?
- Prove that the entropy of mixing of an ideal mixture has aninfinite slope, when plotted vs. x, at x = 0 and x = l.1. The Helmholtz function of a certain gas is given by (V – nb)T — пb)TZ an? F(T,V) = -nRT|1+ In пф V where n is the number of moles of gas, T is the temperatures of the gas, V is the volume of the gas, and a, b, and o are constants. (a) Derive the equation of state, the entropy, and the internal energy of the gas. (b) Suppose that 100 moles of the gas expands from 2 mở to 5 m3 at 280 K and that the constants have the values a = 0.364 J m3 mol-2, b = 4.27 x 10-5 m³ mol-1, and $ = 1.09 x 10-5 m³ K³/2 mol-1. Calculate: ()) Δυ. (ii) the maximum energy that can be made available for work due to the process. (iii) the speed of sound in the gas after the expansion if the ratio of specific heat capacities for the gas is y = 1.28 and the density of the gas is 0.881 kg m-3 in the final state. (c) Using the free energy of a monatomic ideal gas, derive the ideal gas law.Calculate the change in entropy on converting a mole of a gas occupying 20 liters at a pressure of 2 x 10° N/m² to occupying 50 liters at a pressure of 5 x 105 N/m2. Given R = 8.4 J mol 1.K¯1 and Cyv = 21J mol1. K-1.
- En: The latent heat of vaporization of water at 100 °C is 40.6 kJ mol-1and when 1 mol of water is vaporized at 100 °C and 1 atm pressure, the volume increase is 30.19 dm3. Calculate the work done by the system, the change in internal energy AU, the change in Gibbs' energy AG and the entropy change AS.Find the change in entropy of a monoatomic Van der Waals gas using the equation of state nRT an² an² P = and U = nRT V-nb V2 V (Hint: Start from AU = TAS-pdV)A sample containing 3.65 mol of a monatomic ideal gas is heat- ed from 289 K to 458 K, and the entropy remains constant. If the initial volume of the sample was 0.0980 m', by what factor did the pressure increase or decrease during this process? .
- The initial temperature and pressure for one mole of an ideal gas is (Cv = 5 cal mol-1 deg-1) 27oC and 1 atm. Pressure is increased reversibly to 5.3 atm and the temperature is incremented to 90 oC. Calculate the entropy of the process. R = 2 cal mol-1deg-1 answer in cal deg-1The boiling point of compound X is 12° C and its enthalpy of vaporization is 24.6 KJ/mole. What is the entropy (in Joules/mole) of vaporization for this compound?(NOTE: express answer in the NEAREST WHOLE NUMBERS)5RT3 a. A piece of metal of molar heat capacity Cp is heated from 300K to 500K at 2 constant pressure. Calculate the change of entropy, assuming the volume change is negligible.