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13/14 Semester 2 Physical Chemistry I (TKK-2246) Instructor: Rama Oktavian Email: [email protected] Office Hr.: M.13-15, Tu. 13-15, W. 13-15, Th. 13-15, F. 09-11 Outlines 1. Expansion work 2. Multistage expansion 3. Work of expansion 4. Maximum and minimum work Review 1. Suggest a system, boundary, and surroundings for 10 moles of propane gas in a rigid metal cylinder 2. Suggest a system, boundary, and surroundings for 500 mL of water in an open beaker. Review 1. Describe three commonplace examples of how work is done on or by a system 2. A plumber of mass 65 kg carries a toolbox of mass 15 kg to a fifth floor walkup apartment 15 m above ground level. Calculate the work required for this process 3. Describe the internal energy change and work performed when a spring is compressed or expanded. 1st law of thermodynamics Mathematical statement for The 1st Law of Thermodyamics ΔU = q + w in which w > 0 or q > 0 if energy is transferred to the system as work or heat and w < 0 or q < 0 if energy is lost from the system as work or heat Heat, work, and energy Work (W) - any quantity that flows across the boundary of a system during a change in its state Ex: - gas that pushes out a piston and raises a weight - A chemical reaction that drives an electric current through a resistance also does work Expansion work the work arising from a change in volume Ex: - the work done by a gas as it expands and drives back the atmosphere - The term ‘expansion work’ also includes work associated with negative changes of volume, that is, compression Expansion work General expression of expansion work the work required to move an object a distance dz against an opposing force of magnitude F is dw Fdz Expansion work General expression of expansion work dw Fdz F p ext A dw p ext Adz dV Adz dw p ext dV the work arising from a change in volume Expansion work General expression of expansion work dw p ext dV Integrating equation from initial to final volume Vf w p Vi ext dV Expansion work Reversible expansion In a reversible process the system is at equilibrium at every stage of the process Reversibility during pressure changes ensures that p ext p the pressure on the inside of the container is always equal to the pressure exerted on the outside of the container Expansion work Reversible expansion When we set pex = p p ext p the pressure on the inside of the container is always equal to the pressure exerted on the outside of the container dw p ext dV pdV The total work of reversible expansion is therefore Vf w rev pdV Vi Expansion work Isothermal reversible expansion Consider the isothermal, reversible expansion of an ideal gas pV nRT the work of reversible isothermal expansion of a perfect gas from Vi to Vf at a temperature T is Vf w rev nRT Vi dV V nRT ln Vf Vi Expansion work Isothermal reversible expansion Expansion work Isothermal reversible expansion Multistage expansion work Multistage irreversible isothermal expansion and compression n W Wn n 1 where n is number of stage Maximum and minimum work Reversible processes actually do not occur in nature They are simply idealization of actual Processes Easy to analyze Serve as idealized model Maximum and minimum work when Reversible processes are approximated instead of the Actual ones Work-producing devices such as car engine and gas or steam turbine deliver the maximum work, and Work-consuming devices such as compressors, fan, and pumps Consume the minimum work. Exercise A chemical reaction takes place in a container of cross-sectional area 50.0 cm2. As a result of the reaction, a piston is pushed out through 15 cm against an external pressure of 121 kPa. Calculate the work done by the system Exercise Isothermal compression A sample consisting of 2.00 mol He is expanded isothermally at 22°C from 22.8 dm3 to 31.7 dm3 (a) reversibly, (b) against a constant external pressure equal to the final pressure of the gas. For the two processes calculate w Exercise Isothermal compression, maximum and minimum work Three moles of an ideal gas are compressed isothermally from 60 L to 20 L using a constant pressure of 5 atm. Calculate W. If that gas is compressed reversibly, calculate W