## 2 Thermodynamics and Operational Conditions of the Proposed System
### Thermodynamics Models and Equations
#### 2.2.2 Thermodynamics Equations  
First law modelling  
1. Pump (1\(\rightarrow\)2): The power consumed by the pump can be calculated as \[W_{pump}=m_{f1}(h_{2}-h_{1}).\] (2)  
Figure 3: Temperature and heat content available in exhaust gas under different loads.  
The isentropic efficiency of the pump can be calculated as \[\eta_{pump,is}=\frac{h_{2 is}-h_{1}}{h_{2}-h_{1}}.\] (3)
2. Evaporator-ORC (2\(\rightarrow\)3, 5\(\rightarrow\)6): The heat transferred in the evaporator-ORC can be calculated as \[Q_{cwa,ORC}=m_{f1}(h_{3}-h_{2}),\] (4) \[Q_{cwa,ORC}=m_{g}(h_{5}-h_{6}).\] (5)
3. Expander (3\(\rightarrow\)4): The power generated in the expander can be calculated as \[W_{exp}=m_{f1}(h_{3}-h_{4}).\] (6) The isentropic efficiency of the expander can be calculated as \[\eta_{exp,is}=\frac{h_{3}-h_{4}}{h_{3}-h_{4 is}}.\] (7)
4. Condenser-ORC (4\(\rightarrow\)1, 0\(\rightarrow\)12): The heat transferred in condenser-ORC can be calculated as \[Q_{cond,ORC}=m_{f1}(h_{4}-h_{1}),\] (8) \[Q_{cond,ORC}=m_{w1}(h_{12}-h_{0}).\] (9)
5. Compressor (7\(\rightarrow\)8): The power consumed by compressor can be calculated as \[W_{com}=m_{f2}(h_{8}-h_{7}),\] (10) \[W_{com}=W_{exp}.\] (11) The isentropic efficiency of the compressor can be calculated as \[\eta_{com,is}=\frac{h_{8 is}-h_{7}}{h_{8}-h_{7}}.\] (12)
6. Condenser-VCC (8\(\rightarrow\)9, 0\(\rightarrow\)11): The heat transferred in the condenser-VCC can be calculated as \[Q_{cond,VCC}=m_{f2}(h_{8}-h_{9}),\] (13) \[Q_{cond,VCC}=m_{w2}(h_{11}-h_{0}).\] (14)
7. Expansion valve (9\(\rightarrow\)10): The working fluid flowing through the expansion valve can be taken as an isenthalpic throttling process \[h_{9}=h_{10}.\] (15)* Evaporator-VCC (10\(\rightarrow\)7, 13\(\rightarrow\)14): The heat transferred in the evaporator-ORC can be calculated as \[Q_{cau,VCC}=m_{f2}(h_{7}-h_{10}),\] (16) \[Q_{cau,VCC}=m_{air}(h_{13}-h_{14}).\] (17) Second law efficiency The exergy at state point \(i\) in the system can be defined by \[E_{i}=m_{f}[(h_{i}-h_{0})-T_{0}(s_{i}-s_{0})].\] (18) The exergy destruction caused in each component can be calculated as \[I_{i}=\sum E_{in}-\sum E_{out}.\] (19) Expressions for exergy destruction are shown in following: Pump-ORC: \[I_{pump,ORC}=W_{pump}+E_{1}-E_{2}.\] (20) Evaporator-ORC: \[I_{cau,ORC}=E_{5}+E_{2}-(E_{6}+E_{3}).\] (21) Expander-ORC: \[I_{exp,ORC}=E_{3}-E_{4}-W_{exp}.\] (22) Condenser-ORC: \[I_{cond,ORC}=E_{0}+E_{4}-(E_{1}+E_{12}).\] (23) Compressor-VCC: \[I_{com,VCC}=W_{com}+E_{7}-E_{8}.\] (24) Condenser-VCC: \[I_{cond,VCC}=E_{8}+E_{0}-(E_{11}+E_{9}).\] (25) Expansion Valve: \[I_{val,VCC}=E_{9}-E_{10}.\] (26) Evaporator-VCC: \[I_{cau,VCC}=E_{10}+E_{13}-(E_{7}+E_{14}).\] (27) The total exergy destruction caused in this system can be expressed as \[I_{total}=I_{cau,ORC}+I_{exp,ORC}+I_{pump,ORC}+I_{cond,ORC}+I_{cond,VCC}+I_{ val,VCC}+I_{env,VCC}+I_{com,VCC}.\] (28)  
The exergy efficiency of the ORC-VCC waste heat recovery system can be calculated as the following:  
\[\eta_{ex-WHR}=E_{out}/E_{in}. \tag{29}\]  
In this case, the exergy input \(E_{in}\) included the exergy difference of exhaust gas stream, the power of the pump.  
\[E_{out}=(T_{0}/T_{cabin,in}-1)Q_{cau-VCC}, \tag{30}\]  
\[E_{in}=E_{exh}+W_{pump}. \tag{31}\]The term \(EER\) (energy efficiency ratio) is a ratio of the useful cooling provided to the work required of air conditioners. Higher \(EER\) equates to lower operating costs.  
\[EER=\frac{Q_{\textit{cra,VCC}}}{W_{\textit{exp}}}. \tag{32}\]