Question

Refrigerant-134a at \(1 \mathrm{MPa}\) and \(100^{\circ} \mathrm{C}\) is throttled to a pressure of 0.8 MPa. Determine the reversible work and exergy destroyed during this throttling process. Assume the surroundings to be at \(30^{\circ} \mathrm{C}\)

Short answer

Answer: The reversible work during the throttling process is 0. The exergy destroyed during the throttling process can be calculated using the equation \(Ex_{destroyed} = T_{0} \cdot (S_2 - S_1)\), where the values of \(S_1\), \(S_2\), and \(T_{0}\) are determined using the given conditions and thermodynamic tables.

Step-by-step solution

Determine initial conditions

As given in the problem statement, the initial pressure \(P_1\) is \(1\) MPa and the initial temperature \(T_1\) is \(100^{\circ} \mathrm{C}\) (\((100+273.15)\) K). Using the temperature and pressure data, we can find the necessary thermodynamic properties of Refrigerant-134a.

Determine final conditions

The problem statement specifies that the Refrigerant-134a is throttled to a final pressure of \(0.8\) MPa. In a throttling process, there is no heat transfer or work done, thus we can conclude that enthalpy remains constant, \(h_1 = h_2\). With this, we can use a thermodynamic table for Refrigerant-134a to find its final temperature \(T_2\) and other properties based on these conditions.

Determine reversible work

Since the throttling process is an isenthalpic process (constant enthalpy), the reversible work \(W_{rev}\) can be calculated using the following equation derived from the first law of thermodynamics: \(W_{rev} = h_2 - h_1 + q\) Since \(h_1 = h_2\) and \(q=0\) in a throttling process, \(W_{rev} = 0\)

Determine exergy destroyed

To calculate the exergy destroyed during the throttling process, we can use the following equation derived from the second law of thermodynamics: \(Ex_{destroyed} = T_{0} \cdot \Delta S_{gen}\) Here, \(T_{0}\) is the surrounding temperature, which is given as \(30^{\circ} \mathrm{C}\) (\((30+273.15)\) K) and \(\Delta S_{gen}\) is the entropy generated during the process. Since the throttling process is irreversible, entropy is generated, and we can calculate \(\Delta S_{gen}\) using the following equation: \(\Delta S_{gen} = S_2 - S_1\) We can find the values of \(S_1\) and \(S_2\) using the thermodynamic tables for Refrigerant-134a at the given initial and final conditions. Now we can calculate the exergy destroyed as: \(Ex_{destroyed} = T_{0} \cdot (S_2 - S_1)\)

Conclusion

In conclusion, the reversible work done during the throttling process is \(0\). The exergy destroyed during the throttling process can be calculated using the equation \(Ex_{destroyed} = T_{0} \cdot (S_2 - S_1)\), where the values of \(S_1\), \(S_2\), and \(T_{0}\) are determined using the given conditions and thermodynamic tables.