The air$-$conditioning system for your home uses a refrigeration system to cool the indoor air. The refrigeration system uses R$-22.$ It is summer and the system is not cooling the house, so you called an air$-$conditioning service company to come troubleshoot the system. The technician measures two pressures and quickly decides he needs to charge you $\backslash (\backslash$$ $600\mathrm{.}00\backslash )$ to add more refrigerant to the system.

You know that if the system is working properly, the evaporator temperature should not be below $\backslash (32^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash )($freezing point of water$),$ otherwise the water condensing from the air going through the system will freeze on the evaporator and eventually plug up the air flow. You also know something about refrigeration systems from your Thermo II course.

The two pressures he measured are $\backslash (50\backslash$mathrm$\{$lbf$\}/\backslash$mathrm$\{$in$\}^\{2\}\backslash )$ and $\backslash (300\backslash$mathrm$\{$lbf$\}/\backslash$mathrm$\{$in$\}^\{2\}\backslash ).$

a$.$ Based on your knowledge, is there anything wrong with the refrigeration system? Explain.

b$.$ Are you going to have to pay the $\backslash (\backslash$$ $600\mathrm{.}00\backslash )$ to get the system fixed? Explain.