The conservation of energy principles reduces to conserving mechanical energy alone in case of

Explanation:

Conservation of Energy in Mechanical Systems

• The conservation of energy principle states that energy can neither be created nor destroyed; it can only be transformed from one form to another. In the context of mechanical systems, this principle reduces to conserving mechanical energy when the system operates under certain idealized conditions. Mechanical energy includes kinetic energy and potential energy, both of which are associated with the motion and position of objects, respectively.
• In fluid systems, this principle is applied with considerations for the compressibility and thermodynamic properties of the fluid. The specific case where the conservation of energy simplifies to the conservation of mechanical energy alone depends on the fluid's characteristics and processes.

Option 2: Isothermal fluid

• When a fluid undergoes an isothermal process, its temperature remains constant throughout the process. This condition implies that the internal energy of the fluid does not change because internal energy for most fluids is predominantly a function of temperature. Since there is no change in internal energy, the energy transformations are limited to mechanical forms, such as kinetic energy and potential energy. In this case, heat transfer occurs to maintain the constant temperature, but it does not contribute to a change in internal energy.

Under these conditions, the conservation of energy principle reduces to the conservation of mechanical energy alone. This is because the fluid's thermodynamic properties do not involve changes in internal energy, and the work done by or on the fluid is directly related to its mechanical energy.

Mathematical Explanation:

For a fluid undergoing an isothermal process, the first law of thermodynamics is expressed as:
Q = W

Here:

• Q = Heat transfer
• W = Work done

Since the internal energy change (ΔU) is zero in an isothermal process, the energy balance simplifies to the work done being equal to the heat transfer. Therefore, the focus shifts solely to the mechanical energy aspects, such as kinetic and potential energy changes, aligning with the conservation of mechanical energy.