The working substance of a certain Carnot engine is 1.00 mol of an ideal monatom
ID: 1528861 • Letter: T
Question
The working substance of a certain Carnot engine is 1.00 mol of an ideal monatomic gas. During the isothermal expansion portion of this engine's cycle, the volume of the gas doubles, while during the adiabatic expansion the volume increases by a factor of 5.7. The work output of the engine is 990 J in each cycle.
Compute the temperatures of the two reservoirs between which this engine operates.
Express your answer using two significant figures. Enter your answers numerically separated by a comma.
TL,TH = ? Kelvin
Explanation / Answer
in isothermal process w = RTh ln(vf/vi) = RTh ln(2v/vi) = RTh ln2 = Qh
e = 1-TC/TH = wnet/Qh
wnet = Qh(1-TC/TH) = RTh ln2*(1-TC/TH)
in adiabatic gamma = cp/cv = 5/3
TV^(gamma-1) = constant
TH/TC = 5.7^2/3
TC/TH = 0.311
990 / 8.314*ln2*(5.7^2/3 -1) = TC
TC = 77.83 K
TH = 5.7^2/3*TC = 249.83 K
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