- #1
AriAstronomer
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Thermo Efficiency question!
Figure P22.53 represents n mol of an ideal monatomic
gas being taken through a cycle that consists of two
isothermal processes at temperatures 3Ti and Ti and two
constant-volume processes. For each cycle, determine, in terms of n, R, and Ti , (a) the net energy transferred
by heat to the gas and (b) the efficiency of an engine
operating in this cycle.
Now, I've solved part a), and get W = 2nRTln2 (difference between top and bottom portions), can't get part b). I know that efficiency = energy sought/ energy cost = W/Q_h, but they don't really specify in the question where the energy intake is, or energy cost. The answer is 0.273... I've found that for each cycle:
the sides both equal dU = dQ = 3nRT, the top Q = 3nRTln2, bottom Q = nRTln2. Seems like the 'energy cost' based on e = .273 and W = 2nRTln2 should be 3+3ln2, no idea how that comes about though... perhaps somehow the 'cost' is over the top and side??
Ari
Homework Statement
Figure P22.53 represents n mol of an ideal monatomic
gas being taken through a cycle that consists of two
isothermal processes at temperatures 3Ti and Ti and two
constant-volume processes. For each cycle, determine, in terms of n, R, and Ti , (a) the net energy transferred
by heat to the gas and (b) the efficiency of an engine
operating in this cycle.
Homework Equations
The Attempt at a Solution
Now, I've solved part a), and get W = 2nRTln2 (difference between top and bottom portions), can't get part b). I know that efficiency = energy sought/ energy cost = W/Q_h, but they don't really specify in the question where the energy intake is, or energy cost. The answer is 0.273... I've found that for each cycle:
the sides both equal dU = dQ = 3nRT, the top Q = 3nRTln2, bottom Q = nRTln2. Seems like the 'energy cost' based on e = .273 and W = 2nRTln2 should be 3+3ln2, no idea how that comes about though... perhaps somehow the 'cost' is over the top and side??
Ari