3900_2011_PS3 - Problem Set 3 Chem 3900: Physical Chemistry...

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Unformatted text preview: Problem Set 3 Chem 3900: Physical Chemistry II Spring 2011 Grade-it-yourself homework Answers will be posted Tuesday, Feb 15th Problem 1. Exercise 19‐1 in McQ&S. Problem 2. 0.2 moles of an ideal gas at pressure p = 1.00 bar is confined to a cylinder by a piston. The apparatus is thermostatted at T = 300 K. A weight of mass m is placed on the piston, and the gas expands until its pressure has dropped to 0.80 bar, lifting the mass through a height of 0.500 m. i) What is the largest value that the mass m can have in this process? ii) After the expansion is complete, we remove the mass m and replace it with a weight of larger mass m’. The piston now falls back through 0.500 m, compressing the gas, and returning the gas to its initial thermodynamic state. What is the smallest value that m’ can have in this process? iii) Assuming that m has its maximum value, and m’ its minimum value, compute the total thermodynamic work for this cyclical process. iv) Is net work done by the system, or on the system, or is no work done? v) Draw a qualitative graph on a pV plot that illustrates what you have found. We will see later that your result is a consequence of the Second Law of Thermodynamics. Problem 3. A car tire contains air at p = 3.20 bar and T = 300 K. The valve stem is removed, and the air is allowed to expand against the constant atmospheric pressure of p = 1.00 bar, until the pressure is the same inside and outside the tire. This expansion may be treated as adiabatic, because it occurs very rapidly. Air may be treated as an ideal gas with Cv = 5/2 R per mole. i) Calculate the final temperature of the air in the tire. 1 ii) Determine w per mole of air for this process. The system is defined as the air initially in the tire. Problem 4. One mole of an ideal gas is taken around a 3‐stage reversible cycle: Stage I is an isothermal expansion at temperature T from (p1,V1) to (p2,V2) with V2 > V1. Stage II is a change of state at constant volume, from (p2,V2) to (p1,V2). Stage III is a change of state at constant pressure, from (p1,V2) to (p1,V1). i) Draw a diagram representing the cycle in the pV‐plane. For each of the 3 stages of the cycle, derive expressions for q, w, U and H. Present your results in the form of a Table. Indicate for each quantity whether it is positive or negative (if nonzero). Take CV to be independent of temperature. ii) Problem 5. Exercise 19‐28 in McQ&S. After working the problem, show that if Cp ‐ Cv= nR for an ideal gas, then (H / p )T 0 for that gas. 2 ...
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