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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Chemistry 5.60 Physical Chemistry Problem Set #2 Readings: SAB, Chapter 2.9-2.13 2.1 A sample of nitrogen of mass 3.12 g at 23.0 C is allowed to expand reversibly and adiabatically from 400 mL to 2.00 L. What is the work done by the gas? (Assume ideal gas behavior.) 2.2 A sample consisting of 1 mole of a monatomic ideal gas (for which 3 2 V CR ) is taken through the cycle shown in the figure below. (a) Determine the temperature at 1, 2, and 3. (b) Calculate q, w, U and H for each step and for the overall cycle. If a numerical answer cannot be obtained from the information given, then write in + (positive), - (negative), or ? (can’t tell) as appropriate. 2.3 When a system is taken from state A to state B along the path ACB in the figure below, 80 J of heat flows into the system and the system does 30 J of work. (a) How much heat flows into the system along path ADB if the work done is 10J? (b) When the system is returned from state B to A along the curved path, the work done on the system is 20J. Does the system absorb or liberate heat, and how much? (c) If U D – U A = +40J, find the heat absorbed in the processes AD and DB.
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2.4 Show that d q d U P d T C V d T RT d ln V is not an exact differential, but d q T C V d ln T R d ln V is an exact differential. 2.5 An ideal gas expands reversibly and isothermally from 10 bar to 1 bar at 298.15 K. What are the values of ( a ) w per mole, (b) q per mole, ( c ) U and ( d ) H ? ( e ) If the ideal gas expands instead from 10 bar to 1bar at 298.15 K isothermally against a constant pressure of 1 bar. How much work is done on the gas? 2.6 True or False . Give a brief explanation for each and if false provide a counter example: (a) The enthalpy of a system is always greater than its internal energy. (b) In the reversible isothermal expansion of a real gas, the energy remains constant. (c) In the reversible adiabatic expansion of a real gas, the enthalpy always decreases. (d) At a given temperature and volume, the pressure of one mole of a real gas is always less than the pressure of one mole of an ideal gas.
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