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Chapter 6: Problem 9

Would a nuclear power plant violate either the first law or the second law of thermodynamics? Explain.

Short Answer

Expert verified
No, a nuclear power plant does not violate either the first or the second law of thermodynamics.

Step by step solution

01

Understanding the First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. A nuclear power plant converts nuclear energy into electrical energy, so it abides by this law as it does not create or destroy energy.
02

Analyzing the Second Law of Thermodynamics

The Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time. In other words, processes occur in the direction of increasing disorder. A nuclear power plant generates waste heat during energy conversion, thus increasing the entropy of the surroundings. This also adheres to the second law.
03

Examining Practical Implications

Real-world power plants are not perfectly efficient and always produce some form of energy loss, typically as heat. This inefficiency and the resultant increase in entropy are consistent with the second law. Moreover, they do not violate the first law, as they only convert energy types.
04

Conclusion

A nuclear power plant does not violate either the First Law or the Second Law of Thermodynamics. It converts nuclear energy into electrical energy without creating or destroying energy (observing the first law) and increases the entropy of the surroundings (observing the second law).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

First Law of Thermodynamics
The First Law of Thermodynamics is a fundamental principle in physics. It states that energy cannot be created or destroyed; it can only change forms. In a nuclear power plant, nuclear energy is converted into electrical energy. This conversion aligns perfectly with the first law because the total amount of energy remains constant.

For example:
  • Nuclear energy in the reactor is converted into thermal energy.
  • Thermal energy then transforms into mechanical energy as it drives the turbines.
  • Finally, mechanical energy changes into electrical energy via the generator.
At each stage, energy is not lost but transformed, demonstrating the conservation principle of the First Law of Thermodynamics.
Second Law of Thermodynamics
The Second Law of Thermodynamics revolves around the concept of entropy. It states that the total entropy of an isolated system can never decrease over time. This means that natural processes tend to move towards a state of higher disorder or randomness.

In the case of a nuclear power plant, while converting nuclear energy into electrical energy, some energy is inevitably lost as waste heat, contributing to an overall increase in entropy.

Core ideas:
  • Energy conversion processes are never 100% efficient.
  • Waste heat production is a manifestation of increased entropy.
  • The second law ensures these processes flow irreversibly towards higher entropy.
This law dictates that energy transformations, like those in a power plant, should increase the system's total entropy, proving the plant's adherence to this thermodynamic rule.
Entropy
Entropy is a measure of disorder or randomness in a system. In thermodynamics, entropy helps predict the direction of energy transformations. According to the Second Law of Thermodynamics, entropy of an isolated system never decreases. In real-world applications, this means that processes tend to become more disordered over time.

Nuclear plants generate a significant amount of waste heat, adding to the surrounding environment's entropy.
Key points to understand:
  • Entropy increases when energy is transformed from one form to another.
  • Waste heat is a common byproduct of energy conversion, contributing to higher entropy.
  • In a nuclear power plant, increasing entropy is an inevitable outcome of generating electrical power.
Understanding entropy is crucial in recognizing why complete efficiency in energy systems is impossible.
Energy Conversion
Energy conversion is the process of changing energy from one form to another. In a nuclear power plant, this involves several stages, each transforming nuclear energy into usable electrical power. These stages include:
  • Nuclear reactions generating heat within the reactor.
  • Heat converted to steam, driving turbines.
  • Turbine motion transformed into electrical energy by generators.
This series of conversions highlights the principle that energy, while changing form, is conserved according to the First Law of Thermodynamics. Waste heat from these conversions also embodies the Second Law by adding to the overall increase in entropy.
Waste Heat
Waste heat is energy released into the environment that is not converted into useful work. In thermodynamic processes, like those in a nuclear power plant, waste heat is a natural byproduct. Despite efforts to increase efficiency, some energy always escapes as heat due to the intrinsic limitations explained by the Second Law of Thermodynamics.

Considerations include:
  • Every energy conversion stage produces some waste heat.
  • Increased entropy results from this waste, aligning with the second law.
  • Managing waste heat is essential for operational efficiency and environmental protection.
Waste heat demonstrates the practical implications of thermodynamic laws and the challenges of achieving higher efficiency in energy conversion systems.

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Most popular questions from this chapter

A storage battery is connected to a motor, which is used to lift a weight. The battery remains at constant temperature by receiving heat from the outside air. Is this a violation of the second law? Why?

There are many paramagnetic solids that have internal energies which depend only on temperature, like an ideal gas. In an isothermal decrease of the magnetic field, heat is absorbed from one reservoir and converted completely into work. Is this a violation of the second law? Explain.

A vessel contains \(10^{-3} \mathrm{~m}^{3}\) of helium gas at \(3 \mathrm{~K}\) and \(10^{3} \mathrm{~Pa}\). Take the zero of internal energy of helium to be at this state. (a) The temperature is raised at constant volume to \(300 \mathrm{~K}\). Assuming helium to behave like an ideal monatomic gas, how much heat is absorbed, and what is the internal energy of the helium? Can this energy be regarded as the result of heating or working? (b) The helium is now expanded adiabatically to \(3 \mathrm{~K}\). How much work is done, and what is the new internal energy? Has heat been converted to work without compensation, thus violating the second law? (c) The helium is now compressed isothermally to its original volume. What are the quantities of heat and work in this process? What is the thermal efficiency of the cycle? Plot the cycle on a \(P V\) diagram.

An imaginary ideal-gas engine operates in a cycle, which forms a rectangle with sides parallel to the axes of a \(P V\) diagram. Call \(P_{1}\) and \(P_{2}\) the lower and higher pressures, respectively; call \(V_{1}\) and \(V_{2}\) the lower and higher volumes, respectively. (a) Calculate the work done in one cycle. (b) Indicate which parts of the cycle involve heat flow into the gas, and calculate the amount of heat flowing into the gas in one cycle. (Assume constant heat capacities.) (c) Show that the efficiency of this engine is $$ \eta=\frac{\gamma-1}{\frac{\gamma P_{2}}{P_{2}-P_{1}}+\frac{V_{1}}{V_{2}-V_{1}}} $$

In the tropics, the water near the surface is warmer than the deep water. Would an engine operating between these two levels violate the second law? Why?
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