Examples Systems with Finite Rates of Heat Exchange

3 Examples Systems with Finite Rates of Heat Exchange 

One rather simple but straightforward illustrative example is a system that does work but differs from ideal reversible engines by exchanging heat with its reservoirs at finite rates, given by a linear relation. 

In carrying out this analysis, it is often convenient to choose as the control variable the system s temperature T. One might alternatively choose the reservoir temperature but the analysis is easier if we use T, and it can be controlled in practice by making small adiabatic adjustments along the path of the process. We assume that such adjustments require only infinitesimal times. 

The analysis begins with a basic theorem For this system, minimum entropy production implies a constant rate of entropy production on each branch of the cycle. In the limit of a slow process, this rate is the same for all branches of the cycle. A second theorem follows Suppose the total cycle time is t, that the entropy produced on the ith branch of the cycle is 7, and that k is the maximum of the heat conductances on all branches. Then a lower bound for the entropy production, per cycle, is 

Furthermore the work such a system can produce is also boimded  

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