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

An ideal Carnot engine operates between a heat reservoir and a block of ice of mass M. An external energy source maintains the reservoir at a constant temperature [itex]T_{h}[/itex]. At time t=0 the ice is at its melting point [itex]T_{0}[/itex], but it is insulated from everything except the engine, so it is free to change state and temperature. The engine is operated in such a way that it extracts heat from the reservoir at a constant rate [itex]P_{h}[/itex].

(a) Find an expression for the time [itex]t_{1}[/itex] at which all the ice is melted, in terms of the quantities given and any other thermodynamic parameters.

(b) Find an expression for the mechanical power output of the engine as a function of time for times [itex]t > t_{1}[/itex].

2. Relevant equations

[tex]Q=ML_{f}[/tex]

[tex]W=Q_{h}-Q_{c}[/tex]

[tex]\frac{dQ_{h}}{dt}=\frac{dQ_{c}}{dt} + \frac{dW}{dt}[/tex]

3. The attempt at a solution

First of all I assumed

[tex]\frac{dW}{dt}=0[/tex]

so

[tex]\frac{dQ_{h}}{dt}=\frac{dQ_{c}}{dt}= P_{h}[/tex]

[tex]\int dQ_{h} = P_{h}\int dt = P_{h}t_{1} = ML_{f}[/tex]

so

[tex]t_{1} = \frac{ML_{f}}{P_{h}}[/tex]

but somehow to answer manages to squeeze out

[tex]t_{1} = \frac{ML_{f}T_{h}}{P_{h}T_{0}}[/tex]

Whats the deal here? That answer doesn't seem to make much sense since it appears to be saying the hotter the heat reservoir, the longer it takes to melt the ice. I would have thought it to be the other way around.

And for part (b) I am not sure where to start.

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# Homework Help: Ideal carnot engine

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