Atomic Engine Worksheet
High School Physics & Chemistry Nuclear Power Systems
The Atomic Engine: Nuclear Reactor Systems
Student: Date/Period:
Key Concept: Controlled chain reactions, pressurized thermodynamic isolation loops, and turbine electricity generation. PWR Standard
1
Fission Chain Reaction & Core Physics
Thermal Neutron Absorption (\( ^{235}\text{U} \))
Induced Fission Equation
\( ^{235}_{\ 92}\text{U} + ^{1}_{0}\text{n} \to ^{236}_{\ 92}\text{U}^* \to ^{141}_{\ 56}\text{Ba} + ^{92}_{\ 36}\text{Kr} + 3\;^{1}_{0}\text{n} + 200\text{ MeV} \)
\( \Delta m = m_{\text{react}} - m_{\text{prod}} \) \( E = \Delta m c^2 \)
Criticality Factor (\( k \)): Neutron population ratio from generation \( n \) to \( n+1 \).
\( k < 1 \) Sub \( k = 1 \) Critical \( k > 1 \) Super
A. Why must high-velocity fast neutrons (\(\sim 2\text{ MeV}\)) be slowed into thermal neutrons (\(\sim 0.025\text{ eV}\)) by the water moderator?
B. How does inserting or withdrawing neutron-absorbing control rods (Boron/Cadmium) stabilize \( k = 1.00 \)?
2
Pressurized Water Reactor (PWR): The Three Closed Loops
Thermodynamic Isolation
LOOP 1: PRIMARY (NUCLEAR)
Radioactive Core Coolant
Pressurized to ~155 atm to suppress boiling at 315°C. Circulates through fuel bundles & steam generator tubes.
Reactor Vessel ↔ Pressurizer
LOOP 2: SECONDARY (STEAM)
Non-Radioactive Working Fluid
Absorbs heat across tube walls without contact. Vaporizes to high-pressure steam (~70 atm) driving the turbine.
Steam Generator → Turbine
LOOP 3: TERTIARY (COOLING)
Environmental Heat Sink
Draws water from a reservoir or cooling tower into condenser tubes, cooling secondary steam back to liquid.
Condenser ↔ Cooling Tower
| Component | Loop (1, 2, or 3) | Specific Physics Role / Energy Function |
|---|
| 1. Fuel Assemblies (\(\text{UO}_2\)) | Loop ____ | Sustains fission; releases binding energy as kinetic energy of fission fragments |
| 2. Pressurizer | Loop ____ | Maintains 15.5 MPa using electric immersion heaters and spray to prevent water boiling |
| 3. Steam Generator Tubes | Boundary 1 & 2 | Conducts thermal energy across alloy barrier without chemical or isotopic mixing |
| 4. Condenser Heat Exchanger | Boundary 2 & 3 | Causes rapid phase change (\(\text{gas}\to\text{liquid}\)), creating vacuum drop behind turbine |
Radiation Containment Analysis: Why must the primary coolant loop be physically sealed from the secondary loop? What radioactive isotopes would escape into the open turbine hall if a steam generator tube ruptured?
Nuclear Energy Curriculum • Systems & Engineering Turn over for Energy Transformations & Safety Analysis → Page 1 of 2
Thermodynamic Flow & Safety Engineering
Energy Conversions, Electromagnetic Induction & Fail-Safe Physics
Student: Page 2
3
Energy Transformation Pathway
Trace Forms of Energy from Nucleus to Grid
Stage 1: Core
Nuclear Potential Energy
Mass defect converted into kinetic energy of daughter nuclei & neutrons.
Stage 2: Primary Loop
Thermal Energy (Heat)
Collisions heat pressurized water, transferring thermal energy via conduction.
Stage 3: Turbine
Mechanical Kinetic Energy
Expanding superheated steam pushes turbine blades, rotating the central shaft.
Stage 4: Generator
Electrical Energy
Faraday's Induction: Coils rotate through magnetic fields generating AC current.
Thermodynamic Limits: Why cannot 100% of the fission thermal energy be transformed into electrical output? State the governing law of thermodynamics, and identify where the unconverted energy is expelled.
4
Thermal Efficiency & Power Calculations
Thermodynamics: \( \eta = \frac{W_{\text{net}}}{Q_{\text{in}}} \times 100\% \)
Plant Performance Profile: A nuclear power plant core generates \( 3300\text{ MW}_{\text{thermal}} \) (\( Q_{\text{in}} \)). The generator outputs \( 1100\text{ MW}_{\text{electric}} \) (\( W_{\text{net}} \)) to high-voltage transmission lines.
Show Formulas & Units
A. Calculate the plant's overall thermodynamic efficiency (\( \eta \)):
B. Determine the rate of waste heat rejected (\( Q_{\text{out}} \)) to the cooling loop:
5
Critical Thinking: Reactor Safety Engineering
SCRAM & Physics Feedbacks
Scenario A: The SCRAM Emergency Sequence
During an emergency SCRAM, control rods drop into the core via gravity in under 2 seconds, halting fission (\( k \to 0 \)).
Why must emergency coolant pumps continue running for days/weeks after fission stops? (Identify the heat source).
Scenario B: Negative Void Reactivity Coefficient
Water serves as both coolant and moderator. If coolant overheats and boils, forming steam pockets ("voids"):
How does this inherently prevent a runaway thermal explosion? Explain using neutron moderation physics.
Synthesis: Compare a coal-fired thermal plant and a nuclear power plant. Identify ONE identical thermodynamic stage and ONE fundamental difference in the fuel energy density or emissions.
Nuclear Energy Curriculum • Systems & Engineering Standards: NGSS HS-PS1-8 (Nuclear Processes) & HS-PS3-3 (Energy Conversion) Page 2 of 2
