91Ó°ÊÓ

Pump efficiency is a measure of how well a pump converts the input energy (usually electrical) into useful mechanical work that moves fluid. In this exercise, the pump efficiency is given as isentropic efficiency, which is related to the thermal efficiency under ideal conditions. For a pump, isentropic efficiency \(η_p\) is defined as the ratio of the work done during an isentropic process to the actual work done.

In the given problem, the pump's isentropic efficiency is 90%. This means that 90% of the ideal (isentropic) work is being achieved in reality. The remaining 10% is lost to irreversibilities and inefficiencies within the pump. To find the actual exit enthalpy \(h_2\), the formula used is:

\[η_p = \frac{h_{2s} - h_1}{h_2 - h_1} \]
Here, \(h_{2s}\) is the enthalpy at the exit under isentropic conditions, which can be determined using steam tables or property data. Rearranging the formula, we get:

\[ h_2 = \frac{h_{2s} - h_1}{η_p} + h_1 \]
By substituting the known values, the actual enthalpy \(h_2\) can be calculated. This calculation is crucial for finding the power required by the pump.

Exergy destruction refers to the loss of useful work potential in a thermodynamic process due to inefficiencies. This is a key concept in evaluating the real performance of systems and is closely related to entropy generation.

In this problem, the rate of exergy destruction is calculated by first identifying the entropy generation \(S_{gen} = s_2 - s_1\).

Then, exergy destruction (ED) can be determined using the relation:

\[ \text{ED} = T_0 S_{gen} \]
Here, \(T_0\) is the ambient temperature (300 K) and \(S_{gen}\) is the change in entropy between the inlet and exit of the pump. In this exercise, we have:

\[ S_{gen} = s_2 - s_1 = 0.0038 \text{ kJ/kg·K} \]
Thus, exergy destruction is:

\[ \text{ED} = 300 \text{ K} \times 0.0038 \text{ kJ/kg·K} = 1.14 \text{ kJ/kg} \]
This value shows the extent to which the available energy has been degraded due to irreversibilities within the pump.

An isentropic process is a theoretical concept where entropy remains constant. This type of process is idealized and reversible, occurring without any entropy generation. In practical terms, it means there are no losses due to friction, heat transfer, or other inefficiencies. Such a process results in the maximum possible work output or the minimum possible work input for compression or expansion processes.

In the context of the given problem, we assume the pump ideally follows an isentropic process to determine a reference point called the isentropic enthalpy \(h_{2s}\). Given that the initial entropy \(s_1\) remains constant during this ideal process, we find \(h_{2s}\) at 10 MPa and entropy \(s_1 = 0.6493 \text{ kJ/kg·K}\). These values are usually determined using steam tables or specific property data.

The actual process, however, involves some irreversibilities, meaning the exit state will not perfectly reflect these ideal conditions. The real-world deviation from this ideality is quantified by the isentropic efficiency, which is used to interpret the real exit state for comparison.