Throttling Process and Specific Internal Energy:

In a throttling process, the fluid undergoes a sudden expansion or contraction as it passes through a partially open valve. This process is often used to reduce the pressure of a fluid without any significant change in its enthalpy.

The specific internal energy of a fluid is the energy per unit mass due to its molecular structure and composition. It is an intensive property and is usually denoted by the symbol u. The change in specific internal energy during a throttling process can be determined using the first law of thermodynamics, which states that the change in specific internal energy (Δu) is equal to the heat transfer (Q) minus the work done (W) on the system.

Given Data:
- Initial pressure (P1) = 10 bar
- Final pressure (P2) = 1 bar
- Initial specific volume (v1) = 0.5 m³/kg
- Final specific volume (v2) = 2.0 m³/kg

Calculating Change in Specific Internal Energy:

To calculate the change in specific internal energy during the throttling process, we need to determine the initial and final specific internal energies.

The specific internal energy can be determined using the equation:

u = h - Pv

Where h is the specific enthalpy, P is the pressure, and v is the specific volume.

Initial Specific Internal Energy:
Using the given initial specific volume and pressure, we can calculate the initial specific internal energy (u1):

u1 = h1 - P1v1

Final Specific Internal Energy:
Similarly, using the given final specific volume and pressure, we can calculate the final specific internal energy (u2):

u2 = h2 - P2v2

Change in Specific Internal Energy:
The change in specific internal energy (Δu) during the throttling process is given by the difference between the final and initial specific internal energies:

Δu = u2 - u1

Explanation:
To calculate the change in specific internal energy during a throttling process, we need to determine the initial and final specific internal energies. These can be calculated using the specific volume and pressure values before and after throttling. By subtracting the initial specific internal energy from the final specific internal energy, we can determine the change in specific internal energy. This change represents the energy transfer that occurs during the throttling process.