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?Prove that the entropy of mixing of an ideal mixture has aninfinite slope, when plotted vs. x, at x = 0 and x = l.
- A sample consisting of n moles of an ideal gas undergoes a reversible isobaric expansion from volume Vi to volume 3Vi . Find the change in entropy of the gas by calculating ∫fi dQ/T, where dQ = nCP dT.For one component gas that is confined in a box with volume V. V We can get the entropy of the gas as S = Nk, In where N is the total number of atoms, a is the radius of the atom. Can you guess (or work out) how it is obtained?What is the entropy change for 3.20 mol of an ideal monatomic gas undergoing a reversible increase in temperature from 380 K to 425 K at constant volume?
- If one mole of an ideal gas (Cp,m = 5R/2) is expanded isothermally at 300 K until it’s volume tripled, what is the change in entropy of the gas? 5/2 R ln3 3/2 R ln 3 Zero R ln 3Calculate the entropy of fusion of a compound at 25 °c given that its enthalpy of fusion is 36 kJ mol-1 at its melting point of 151 °c and the molar heat capacities (at constant pressure) of the liquid and solid forms are 33 J K-1 mol-1 and 17 J K-1 mol- 1, respectively.Does the internal energy (U) of a perfect gas go up or down with increasing pressure under adiabatic, reversible conditions (i.e. at constant entropy)? Hint: you’re looking for ∂U/∂P)s . and under conditions of constant entropy, the transition must be adiabatic and reversible. As such: ∂U= CV ∂T, and ∂T/∂P )s = V/Cp
- 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-1Starting with the Clausius Inequality, ∂S ≥ ∂q/T, can you prove that, under conditions of constant pressure and entropy, for the total entropy to increase, ∂H ≤ 0 J?A 1.0 mole sample of a “monatomic” ideal gas undergoes a reversible isobaric expansion from Vi to 20Vi. Find the change in entropy of the gas. (dQ = n Cp dT)