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chapter12.3-12.4_slides

chapter12.3-12.4_slides - Isobaric Pressure stays constant...

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11/17/2009 1 Isobaric Pressure stays constant Horizontal line on the PV diagram Isovolumetric Volume stays constant Vertical line on the PV diagram Isothermal Temperature stays the same For ideal gas, Adiabatic No heat is exchanged with the surroundings V nRT P 1 ) ( or constant nRT PV P constant The work done by an expanding gas: Q: For an ideal gas, what is the temperature change during an isobaric expansion? Solution: (ideal gas law) i f P V i V f V V P W env nRT PV T nR V P nR V V P nR V P T i f ) ( Conclusion: Isobaric expansion, T increases; isobaric compression, T decreases

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11/17/2009 2 V constant; Vertical line on PV diagram W = 0 (since V = 0) Q: During an isovolumetric process, the temperature of the gas (in Kelvins) is doubled . How does pressure change? Solution: P V i P f P f f nRT V P i i nRT V P i f i f nRT nRT V P V P 2 i f i f T T P P For an adiabatic process, Q = 0 (no heat exchange) First Law becomes U = W+Q=W Change in internal energy equals to the work done on the gas Q: During an adiabatic compression of 1.0 mol monatomic ideal gas , the temperature of the gas increases from 100 K to 200 K. What is the work done on the gas? Solution: Ideal monatomic gas: T nR U 2 3 nRT U 2 3 J 5 . 1246 ) 100 200 ( 31 . 8 0 . 1 2 3 U J 5 . 1246 U W
11/17/2009 3 T constant Ideal gas: internal energy depends only on temperature. T = 0 U = 0 - no change in internal energy First Law becomes W = - Q - work done on the gas equals to the energy released by heat It can be shown that, for an isothermal process, the work done by a gas to the environment is ) ln( i f env V V nRT W function logarithm natural : ) ln( x A cyclic process is one in which the process originates and ends at the same state U f = U i Q = -W The net work done per cycle by the gas is equal to the area enclosed by the path representing the process on a PV diagram

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11/17/2009 4 Calculate the work done by the gas to the environment during the cyclic process abcda shown on the right.
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chapter12.3-12.4_slides - Isobaric Pressure stays constant...

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