Key Equations

Result of energy conservation	$W=Q_{\text{h}}-Q_{\text{c}}$
Efficiency of a heat engine	$e=\frac{W}{Q_{\text{h}}}=1-\frac{Q_{\text{c}}}{Q_{\text{h}}}$
Coefficient of performance of a refrigerator	$K_{\text{R}}=\frac{Q_{\text{c}}}{W}=\frac{Q_{\text{c}}}{Q_{\text{h}}-Q_{\text{c}}}$
Coefficient of performance of a heat pump	$K_{\text{P}}=\frac{Q_{\text{h}}}{W}=\frac{Q_{\text{h}}}{Q_{\text{h}}-Q_{\text{c}}}$
Resulting efficiency of a Carnot cycle	$e=1-\frac{T_{\text{c}}}{T_{\text{h}}}$
Performance coefficient of a reversible refrigerator	$K_{\text{R}}=\frac{T_{\text{c}}}{T_{\text{h}}-T_{\text{c}}}$
Performance coefficient of a reversible heat pump	$K_{\text{P}}=\frac{T_{\text{h}}}{T_{\text{h}}-T_{\text{c}}}$
Entropy of a system undergoing a reversible process at a constant temperature	$\text{Δ}S=\frac{Q}{T}$
Change of entropy of a system under a reversible process	$\text{Δ}S=S_B-S_A={\displaystyle {\int }_A^{B}dQ\text{/}T}$
Entropy of a system undergoing any complete reversible cyclic process	${\displaystyle \oint dS={\displaystyle \oint \frac{dQ}{T}}}=0$
Change of entropy of a closed system under an irreversible process	$\text{Δ}S\ge 0$
Change in entropy of the system along an isotherm	$\underset{T\to 0}{\text{lim}}{(\text{Δ}S)}_T=0$