## Second Law of Thermodynamics

• ### Units and Variables

• e - thermal efficiency
• W - work done by a heat engine, in Joules
• COP - coefficient of performance
• $e=1-\frac{|{Q}_{c}|}{|{Q}_{h}|}$
• $W=|{Q}_{h}|-|{Q}_{c}|$
• $\text{COP (heating)}=\frac{\left|{Q}_{h}\right|}{W}$
• $\text{COP (cooling)}=\frac{|{Q}_{c}|}{W}$
• ### Carnot Engines

• $\frac{|{Q}_{c}|}{|{Q}_{h}|}=\frac{{T}_{c}}{{T}_{h}}$
• ${e}_{C}=1-\frac{{T}_{c}}{{T}_{h}}$
• $\text{COP (heating)}=\frac{{T}_{h}}{\mathrm{\Delta T}}$
• $\text{COP (cooling)}=\frac{{T}_{c}}{\mathrm{\Delta T}}$
• $e=1-\frac{1}{{\left({V}_{1}/{V}_{2}\right)}^{\left(\gamma -1\right)}}$