Fluid at 10.35 bar having a specific volume of 0.18 m /kg is throttled to a pressure of 1 bar. If the specific volume of the fluid after throttling is 0.107 m3/kg, calculate the change in specific internal energy during the process
The correct answer and explanation is :
In this problem, we are asked to calculate the change in specific internal energy ((\Delta u)) during the throttling process of a fluid. The process involves a reduction in pressure from 10.35 bar to 1 bar, with the specific volume changing from 0.18 m³/kg to 0.107 m³/kg.
Steps to solve the problem:
1. Throttling Process Overview:
A throttling process is an adiabatic, irreversible process in which there is no heat exchange with the surroundings (no heat is added or removed) and no work is done on or by the system. The primary feature of a throttling process is that the enthalpy remains constant (i.e., (h_1 = h_2)).
The change in specific internal energy is related to the change in enthalpy in some cases, but since no work is done and no heat is exchanged, the change in specific internal energy ((\Delta u)) and the change in enthalpy ((\Delta h)) are equivalent for most fluids. Here, we will focus on the change in internal energy, which can be evaluated using the relation between pressure, volume, and internal energy.
2. Enthalpy-Volume-Pressure Relations:
To calculate the change in specific internal energy, we often need thermodynamic tables or equations of state for the fluid, which would provide the specific enthalpy and internal energy at the given pressures and specific volumes. Since this problem does not provide such data, we will assume that we can use the specific volume to estimate the internal energy change directly for this kind of problem.
3. Application of Thermodynamic Relations:
We can approximate the change in internal energy using the specific volume change during throttling. For an ideal gas, the relationship between the change in internal energy and specific volume is given by:
[
\Delta u = \int v \, dP
]
However, for practical purposes, we often rely on tabulated values for specific enthalpy and internal energy changes during throttling. In the absence of detailed fluid properties, the approximate change in specific internal energy ((\Delta u)) can be assumed to be related to the volume change under the given conditions.
4. Solution:
Using the change in specific volume, we can estimate the change in internal energy based on fluid properties, but further details about the exact fluid would be needed to provide a precise value.
For this problem, assuming ideal conditions and the behavior of a real fluid that behaves similarly to an ideal gas, we can conclude that the change in specific internal energy would be directly proportional to the change in volume for the given process.
Final Answer:
The change in specific internal energy can be approximated as proportional to the change in specific volume, but precise calculation requires detailed fluid properties not provided in the problem statement.
