(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

http://img21.imageshack.us/img21/1197/questionof.jpg [Broken]

3. 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 W_{min}?

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# Homework Help: Refrigerator (Thermodynamics)

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