How Do Coal and Nuclear Power Plants Compare in Efficiency and Waste Production?

[phys-unit]

Homework Statement

A typical coal-fired electric power plant has an efficiency of 39.5%, while a nuclear power plant is 33.5% efficient.
(a) How many joules of thermal energy are required by each plant to generate one joule of electrical energy? How much heat does each plant exhaust as waste?

Homework Equations

None that I know :(

The Attempt at a Solution

unsure how to go about this problem, any help is appreciated.

 

[Redbelly98]

Homework Equations

None that I know :(

How do you think the following are related:

• Energy consumed
• Energy generated
• Efficiency

In other words, how is efficiency defined?

 

[tomcue]

I would approach this problem by first understanding the concept of thermal energy and efficiency. Thermal energy refers to the energy associated with the movement of particles in a substance, such as heat. Efficiency, on the other hand, is a measure of how well a system converts energy into useful work. In this case, the efficiency of a power plant refers to how much of the thermal energy is converted into electrical energy.

To answer the first part of the question, we need to calculate the amount of thermal energy required to generate one joule of electrical energy for each type of power plant. This can be done by using the formula for efficiency, which is Efficiency = (Useful energy output / Total energy input) x 100%. Rearranging this formula, we can calculate the total energy input required for one joule of useful energy output. For the coal-fired power plant, this would be (1/0.395) = 2.53 joules of thermal energy. For the nuclear power plant, it would be (1/0.335) = 2.99 joules of thermal energy. This means that the coal-fired power plant requires less thermal energy to generate one joule of electrical energy compared to the nuclear power plant.

For the second part of the question, we need to calculate the amount of heat exhausted as waste by each power plant. This can be done by subtracting the useful energy output from the total energy input. For the coal-fired power plant, this would be (2.53 - 1) = 1.53 joules of heat exhausted. For the nuclear power plant, it would be (2.99 - 1) = 1.99 joules of heat exhausted. This shows that the nuclear power plant exhausts more heat as waste compared to the coal-fired power plant.

In conclusion, the coal-fired power plant requires less thermal energy and exhausts less heat as waste compared to the nuclear power plant. This highlights the importance of improving the efficiency of power plants to reduce energy waste and minimize the impact on the environment. Further research and advancements in energy technology can help increase the efficiency of power plants and reduce our reliance on non-renewable energy sources.