12 - Reversible and Irreversible Processes

12 - Reversible and Irreversible Processes - 93 The Carnot...

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94 The Carnot Cycle P Volume A B C D -work net isothermal isothermal a d i b t c How efficient can this engine be? Efficiency = work out /q in We need to calculate how much work we can get out of this system for a given amount of heat input
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95 The Carnot Cycle P Volume A B C D -work net Work out the various pathways first Isothermal Temp - T H How efficient? A Æ B ¸ ¸ ¹ · ¨ ¨ © § ± A B H AB AB V V nRT q w ln -
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96 The Carnot Cycle P Volume A B C D -work net Work out the various pathways first Isothermal Temp - T H How efficient? B Æ C ± ² H L V BC BC T T nc w U ³ ' q=0 Adiabatic ' T = T H Æ T L
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97 The Carnot Cycle P Volume A B C D -work net Work out the various pathways first Isothermal Temp - T H How efficient? Skipping to D Æ A ± ² L H V DA DA T T nc w U ³ ' q=0 Adiabatic ' T = T L Æ T H ± ² DA H L V BC BC w T T nc w E ³ ³ ³ ' Note that this exactly cancels out w BC
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98 The Carnot Cycle P Volume A B C D -work net pathway C Æ D Isothermal Temp - T L How efficient? ¸ ¸ ¹ · ¨ ¨ © § ± C D L CD CD V V nRT q w ln Since w BC = -w DA , all work is along pathways A Æ B and C Æ D Thus , w BC +w DA = 0
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99 The Carnot Cycle P Volume A B C D -work net How efficient? ¸ ¸ ¹ · ¨ ¨ © § ± ¸ ¸ ¹ · ¨ ¨ © § ² D C L A B H total V V nRT V V nRT w ln ln Why don’t we worry about w BC +w DA contributions? ¸ ¸ ¹ · ¨ ¨ © § ² C D L CD CD V V nRT q w ln ¸ ¸ ¹ · ¨ ¨ © § ² A B H AB AB V V nRT q w ln work net = w AB -w CD
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100 The Carnot Cycle P Volume A B C D -work net D How efficient? ¸ ¸ ¹ · ¨ ¨ © § ± ¸ ¸ ¹ · ¨ ¨ © § ² D C L A B H total V V nRT V V nRT w ln ln 1 2 1 1 2 ² ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § J V V T T Recall that, for an adiabatic process work net = w AB -w CD
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101 The Carnot Cycle P Volume A B C D -work net D How efficient? ¸ ¸ ¹ · ¨ ¨ © § ± ¸ ¸ ¹ · ¨ ¨ © § ² D C L A B H total V V nRT V V nRT w ln ln 1 1 ² ² ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § J A D L H B C L H V V T T and V V T T 1 2 1 1 2 ² ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § V V T T Recall that, for an adiabatic process Thus we can set up the following equalities work net = w AB -w CD
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