- #1
roam
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Homework Statement
http://img21.imageshack.us/img21/1197/questionof.jpg
The Attempt at a Solution
For the first part, if we assume that the cycle is reversible from the 2nd law we have
[itex]\Delta S = \frac{\Delta Q}{T}+S_{gen} = 0[/itex]
And here is the Clasius Inequality
[itex]S_{gen} \geq 0 \implies \frac{\Delta Q}{T} \leq 0[/itex]
[itex]\frac{Q_x}{T_1}-\int^{T_2}_{T_1} \frac{\Delta Q}{T} \leq 0[/itex]
Since ΔQ = dT
[itex]\frac{Q_x}{T_1}-\int^{T_2}_{T_1} \frac{dT}{T} = \frac{Q_x}{T_1}- \ln \frac{T_2}{T_1} \leq 0[/itex]
[itex]T_2 \geq T_1e^{\frac{Q_x}{T_x}}[/itex]
Since we do not know the temprature values we can't make numerical calculation of the lower limit for the final temperature of y. But did I derive the correct equation?
For the second part of the equation, to find the minimum value of work that needs to be supplied to the heat pump I tried to use the 1st Law;
Q − W = U = 0 → W = mcΔT - U
How can we use this to show the above expression for Wmin?
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