Shortcut Methods
Shortcuts and Tricks to Solve Numerical Problems:
1. The efficiency of a Carnot engine is
$$\eta=1-\frac{T_2}{T_1}$$
2. The coefficient of performance of a refrigerator is
$$COP_{refrigerator}=\frac{T_L}{T_H-T_L}$$
3. The change in entropy of the universe for a heat engine is
$$\Delta S_{universe}=\Delta S_{engine}+\Delta S_{reservoirs}=Q_H/T_H-Q_C/T_C-Q_H/T_H$$ $$=-Q_C/T_C=-\frac{Q_C}{T_2}$$ For a refrigerator $$-\frac{Q_C}{T_2}+\frac{Q_H}{T_1}$$
4. The work done by a heat engine per cycle is
$$W=Q_H \eta$$
5. The heat removed by a refrigerator per cycle is
$$Q_C=\frac{T_L}{COP}$$
