A refrigerating machine has been called a ``Heat-pump''; illustrate the meaning of this by describing the action of the Bell-Coleman refrigerating machine. Obtain an expression for the ``coefficient of performance'' of the cycle, and point out the conditions necessary for a high coefficient. If such a refrigerator is driven by a direct acting Carnot engine taking in heat at \(\tau_1\) and rejecting heat at \(\tau_0\), show that the maximum amount of heat which can be taken from the cold chamber at \(\tau_2\) and delivered to the cooling coils at \(\tau_0\), is \[ \frac{\tau_2(\tau_1-\tau_0)}{\tau_1(\tau_0-\tau_2)} \] thermal units for each thermal unit taken in by the Carnot engine at \(\tau_1\).