Ÿ Actual enthalpy at compressor outlet at LTC.

${\eta }_{\text{isen}}=\frac{h_{2s}-h_1}{h_2-h_1}$

Equation (1)

Ÿ Actual enthalpy at compressor outlet at HTC.

${\eta }_{\text{isen}}=\frac{h_{6s}-h_5}{h_6-h_5}$

Equation (2)

Ÿ Mass flow in LTC (heat balance over LTC evaporator)

${\dot{m}}_{\text{LTC}}=\frac{Q_{cc}}{h_1-h_4}$

Equation (3)

Ÿ Mass flow rate in HTC (heat balance over intermediate heat exchanger)

${\dot{m}}_{\text{HTC}}={\dot{m}}_{\text{LTC}}\ast \frac{h_2-h_3}{h_5-h_8}$

Equation (4)

Ÿ Work of LTC compressor (energy balance over LTC compressor)

$W_{LTC,Comp}=m_{LTC}\ast \left(h_2-h_1\right)$

Equation (5)

Ÿ Work of HTC compressor (energy balance over HTC compressor)

$W_{\text{HTC},\text{Comp}}=m_{\text{HTC}}\ast \left(h_6-h_5\right)$

Equation (6)

Ÿ Heat transfer in intermediate heat exchanger (energy balance over entire LTC)

$Q_{\text{int}}=Q_{\text{cc}}+W_{\text{LTC},\text{Comp}}$

Equation (7)

Ÿ Heat rejected by the upper cycle condenser (energy balance over entire HTC)

$Q_{\text{rej}}=Q_{\text{int}}+W_{\text{HTC},\text{Comp}}$

Equation (8)

Ÿ Coefficient of performance (COP)

${\text{COP}}_{\text{LTC}}=\frac{Q_{\text{cc}}}{W_{\text{LTC},\text{Comp}}}$

Equation (9)

${\text{COP}}_{\text{HTC}}=\frac{Q_{\text{int}}}{W_{\text{HTC,Comp}}}$

Equation (10)

${\text{COP}}_{\text{CRS}}=\frac{Q_{\text{CC}}}{W_{\text{HTC,Comp}}+W_{\text{LTC,Comp}}}$

Equation (11)