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Net power developed is a crucial concept in understanding how efficient a power cycle is. It tells you how much usable power is produced by a system after accounting for energy losses. To calculate it, you need to know the thermal efficiency (\text{Eff}) of the system and the rate of energy input (\text{Q}_{\text{in}}). The formula used is: \(\text{P}_{\text{net}} = \text{Q}_{\text{in}} \times \text{Eff}\)In our exercise, the rate of energy input is \(\text{Q}_{\text{in}} = 300 \text{ MW}\)and the thermal efficiency is \(\text{Eff} = 0.333\). Substituting these values into the formula, we get: \(\text{P}_{\text{net}} = 300 \text{ MW} \times 0.333 = 99.9 \text{ MW}\). That means the net power developed is \(99.9 \text{ MW}\). This value is important as it represents the actual amount of power available for use from the power cycle.

The annual net work output is another key parameter that helps you understand the total energy produced by the system over a year. It's important in evaluating how much energy can be harvested for various uses. To find this, you multiply the net power developed by the number of hours the system operates in a year. The formula is: \(\text{W}_{\text{year}} = \text{P}_{\text{net}} \times \text{hours of operation}\)In this exercise, the net power developed is \(\text{P}_{\text{net}} = 99.9 \text{ MW} = 99,900 \text{ kW}\) and the system operates for \(8000 \text{ hours/year}\). Plugging these values into the formula, we get: \(\text{W}_{\text{year}} = 99,900 \text{ kW} \times 8000 \text{ hours/year} = 799,200,000 \text{ kW} \times \text{h/year}\). So, the annual net work output is \(799,200,000 \text{ kW} \times \text{h/year}\). This tells us how much work (or energy) the system produces over a whole year, which is useful for planning and economic analysis.

The value of net work is crucial for understanding the economic benefits of a power system. It helps you determine how much money can be made from the energy produced. To calculate this, you need to multiply the annual net work output by the cost per unit of energy (\text{kW} \times \text{h}). The formula is: \(\text{Value}_{\text{work}} = \text{W}_{\text{year}} \times \text{cost per kW} \times \text{h}\)From our exercise, the annual net work output is \(799,200,000 \text{ kW} \times \text{h/year}\) and the cost per \text{kW} \times \text{h} is \(\text{0.08 \text{ dollars}}\). Substituting these values, we get: \(\text{Value}_{\text{work}} = 799,200,000 \text{ kW} \times \text{h/year} \times 0.08 \text{ dollars} / \text{kW} \times \text{h} = 63,936,000 \text{ dollars/year}\). So, the value of the net work output is \(63,936,000 \text{ dollars/year}\), which represents the potential income generated from the electricity produced by the power cycle.