A nuclear power plant generates 3000 MW of heat energy from nuclear reactions in the reactor's core. This energy is used to boil water and produce high-pressure steam at 300℃. The steam spins a turbine, which produces 1000 MW of electric power, then the steam is condensed and the water is cooled to 25℃ before starting the cycle again. b. What is the plant's actual efficiency?

Verified step by step guidance

1. Calculate the actual efficiency of the power plant using the formula: \( \text{Efficiency} = \frac{\text{Output Energy}}{\text{Input Energy}} \times 100 \% \).
2. Identify the output energy, which is the electrical energy produced by the turbine. In this case, it is 1000 MW.
3. Identify the input energy, which is the heat energy generated from nuclear reactions in the reactor's core. In this case, it is 3000 MW.
4. Substitute the values into the efficiency formula: \( \text{Efficiency} = \frac{1000 \, \text{MW}}{3000 \, \text{MW}} \times 100 \% \).
5. Calculate the efficiency by performing the division and multiplication to find the percentage.

Key Concepts

Thermal Efficiency

Thermal efficiency is a measure of how well a power plant converts heat energy into useful work or electricity. It is calculated by dividing the useful output energy (in this case, electric power) by the input energy (heat energy from nuclear reactions). This concept is crucial for understanding the performance of energy systems and is typically expressed as a percentage.

Energy Conversion

Energy conversion refers to the process of changing energy from one form to another, such as converting thermal energy from boiling water into mechanical energy to spin a turbine. In a nuclear power plant, the heat generated from nuclear fission is used to produce steam, which then drives the turbine. Understanding this process is essential for analyzing how efficiently energy is transformed and utilized.

Heat Transfer

Heat transfer is the movement of thermal energy from one object or substance to another, which occurs in three main ways: conduction, convection, and radiation. In the context of a nuclear power plant, heat transfer is vital for boiling water to create steam and for cooling the steam back into water. This concept is important for evaluating the efficiency of the heat exchange processes within the plant.