HW Key _11 s problems part a

HW Key _11 s problems part a - S37. Calculate W and Q for...

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S37. Calculate W and Q for each of the four steps of a Carnot cycle applied to 1 mole of an ideal gas. Divide the expression that you obtain for total W by Q 2 , and compare the result with - W / Q 2 = (T 2 -T 1 )/T 2 to show that temperatures on the ideal gas scale (those used in your calculation) are proportional to those on the thermodynamic scale (those used in the equation above). By choosing the size of the degree to be the same, the two scales become identical. The Carnot cycle consists of 4 steps. We need to calculate W and Q for each step and then sum them together to find the total heat and work. Step 1 Isothermal expansion W = nRT 2 ln V 2 V 1 Q = nRT 2 ln V 2 V 1 Step 2: Adiabatic expansion W = nC v Δ T = n 3 2 R ( T 1 T 2 ) Q = 0 Step 3: Isothermal compression W = nRT 1 ln V 4 V 3 Q = nRT 1 ln V 4 V 3 Step 4: Adiabatic compression W = nC v Δ T = n 3 2 R ( T 2 T 1 ) Q = 0 Because the process is cyclic, Δ U = 0 and W tot = Q tot . Adding up the work for each of the four steps gives W tot = RT 2 ln V 2 V 1 + 3 2 R ( T 1 T 2 ) RT 1 ln V 4 V 3 + 3 2 R ( T 2 T 1 ) = RT 2 ln V 2 V 1 RT
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This note was uploaded on 02/01/2011 for the course CHEM 111 taught by Professor Owens,g during the Fall '08 term at University of Utah.

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HW Key _11 s problems part a - S37. Calculate W and Q for...

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