Table of contents
- 0. Math Review(0)
- 1. Intro to Physics Units(0)
- 2. 1D Motion / Kinematics(0)
- Vectors, Scalars, & Displacement(0)
- Average Velocity(0)
- Intro to Acceleration(0)
- Position-Time Graphs & Velocity(0)
- Conceptual Problems with Position-Time Graphs(0)
- Velocity-Time Graphs & Acceleration(0)
- Calculating Displacement from Velocity-Time Graphs(0)
- Conceptual Problems with Velocity-Time Graphs(0)
- Calculating Change in Velocity from Acceleration-Time Graphs(0)
- Graphing Position, Velocity, and Acceleration Graphs(0)
- Kinematics Equations(0)
- Vertical Motion and Free Fall(0)
- Catch/Overtake Problems(0)
- 3. Vectors(0)
- Review of Vectors vs. Scalars(0)
- Introduction to Vectors(0)
- Adding Vectors Graphically(0)
- Vector Composition & Decomposition(0)
- Adding Vectors by Components(0)
- Trig Review(0)
- Unit Vectors(0)
- Introduction to Dot Product (Scalar Product)(0)
- Calculating Dot Product Using Components(0)
- Intro to Cross Product (Vector Product)(0)
- Calculating Cross Product Using Components(0)
- 4. 2D Kinematics(0)
- 5. Projectile Motion(0)
- 6. Intro to Forces (Dynamics)(0)
- 7. Friction, Inclines, Systems(0)
- 8. Centripetal Forces & Gravitation(0)
- Uniform Circular Motion(0)
- Period and Frequency in Uniform Circular Motion(0)
- Centripetal Forces(0)
- Vertical Centripetal Forces(0)
- Flat Curves(0)
- Banked Curves(0)
- Newton's Law of Gravity(0)
- Gravitational Forces in 2D(0)
- Acceleration Due to Gravity(0)
- Satellite Motion: Intro(0)
- Satellite Motion: Speed & Period(0)
- Geosynchronous Orbits(0)
- Overview of Kepler's Laws(0)
- Kepler's First Law(0)
- Kepler's Third Law(0)
- Kepler's Third Law for Elliptical Orbits(0)
- Gravitational Potential Energy(0)
- Gravitational Potential Energy for Systems of Masses(0)
- Escape Velocity(0)
- Energy of Circular Orbits(0)
- Energy of Elliptical Orbits(0)
- Black Holes(0)
- Gravitational Force Inside the Earth(0)
- Mass Distribution with Calculus(0)
- 9. Work & Energy(0)
- 10. Conservation of Energy(0)
- Intro to Energy Types(0)
- Gravitational Potential Energy(0)
- Intro to Conservation of Energy(0)
- Energy with Non-Conservative Forces(0)
- Springs & Elastic Potential Energy(0)
- Solving Projectile Motion Using Energy(0)
- Motion Along Curved Paths(0)
- Rollercoaster Problems(0)
- Pendulum Problems(0)
- Energy in Connected Objects (Systems)(0)
- Force & Potential Energy(0)
- 11. Momentum & Impulse(0)
- Intro to Momentum(0)
- Intro to Impulse(0)
- Impulse with Variable Forces(0)
- Intro to Conservation of Momentum(0)
- Push-Away Problems(0)
- Types of Collisions(0)
- Completely Inelastic Collisions(0)
- Adding Mass to a Moving System(0)
- Collisions & Motion (Momentum & Energy)(0)
- Ballistic Pendulum(0)
- Collisions with Springs(0)
- Elastic Collisions(0)
- How to Identify the Type of Collision(0)
- Intro to Center of Mass(0)
- 12. Rotational Kinematics(0)
- 13. Rotational Inertia & Energy(0)
- More Conservation of Energy Problems(0)
- Conservation of Energy in Rolling Motion(0)
- Parallel Axis Theorem(0)
- Intro to Moment of Inertia(0)
- Moment of Inertia via Integration(0)
- Moment of Inertia of Systems(0)
- Moment of Inertia & Mass Distribution(0)
- Intro to Rotational Kinetic Energy(0)
- Energy of Rolling Motion(0)
- Types of Motion & Energy(0)
- Conservation of Energy with Rotation(0)
- Torque with Kinematic Equations(0)
- Rotational Dynamics with Two Motions(0)
- Rotational Dynamics of Rolling Motion(0)
- 14. Torque & Rotational Dynamics(0)
- 15. Rotational Equilibrium(0)
- 16. Angular Momentum(0)
- Opening/Closing Arms on Rotating Stool(0)
- Conservation of Angular Momentum(0)
- Angular Momentum & Newton's Second Law(0)
- Intro to Angular Collisions(0)
- Jumping Into/Out of Moving Disc(0)
- Spinning on String of Variable Length(0)
- Angular Collisions with Linear Motion(0)
- Intro to Angular Momentum(0)
- Angular Momentum of a Point Mass(0)
- Angular Momentum of Objects in Linear Motion(0)
- 17. Periodic Motion(0)
- 18. Waves & Sound(0)
- Intro to Waves(0)
- Velocity of Transverse Waves(0)
- Velocity of Longitudinal Waves(0)
- Wave Functions(0)
- Phase Constant(0)
- Average Power of Waves on Strings(0)
- Wave Intensity(0)
- Sound Intensity(0)
- Wave Interference(0)
- Superposition of Wave Functions(0)
- Standing Waves(0)
- Standing Wave Functions(0)
- Standing Sound Waves(0)
- Beats(0)
- The Doppler Effect(0)
- 19. Fluid Mechanics(0)
- 20. Heat and Temperature(0)
- Temperature(0)
- Linear Thermal Expansion(0)
- Volume Thermal Expansion(0)
- Moles and Avogadro's Number(0)
- Specific Heat & Temperature Changes(0)
- Latent Heat & Phase Changes(0)
- Intro to Calorimetry(0)
- Calorimetry with Temperature and Phase Changes(0)
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes(0)
- Phase Diagrams, Triple Points and Critical Points(0)
- Heat Transfer(0)
- 21. Kinetic Theory of Ideal Gases(0)
- 22. The First Law of Thermodynamics(0)
- 23. The Second Law of Thermodynamics(0)
- 24. Electric Force & Field; Gauss' Law(0)
- 25. Electric Potential(0)
- 26. Capacitors & Dielectrics(0)
- 27. Resistors & DC Circuits(0)
- 28. Magnetic Fields and Forces(0)
- 29. Sources of Magnetic Field(0)
- Magnetic Field Produced by Moving Charges(0)
- Magnetic Field Produced by Straight Currents(0)
- Magnetic Force Between Parallel Currents(0)
- Magnetic Force Between Two Moving Charges(0)
- Magnetic Field Produced by Loops and Solenoids(0)
- Toroidal Solenoids aka Toroids(0)
- Biot-Savart Law (Calculus)(0)
- Ampere's Law (Calculus)(0)
- 30. Induction and Inductance(0)
- 31. Alternating Current(0)
- Alternating Voltages and Currents(0)
- RMS Current and Voltage(0)
- Phasors(0)
- Resistors in AC Circuits(0)
- Phasors for Resistors(0)
- Capacitors in AC Circuits(0)
- Phasors for Capacitors(0)
- Inductors in AC Circuits(0)
- Phasors for Inductors(0)
- Impedance in AC Circuits(0)
- Series LRC Circuits(0)
- Resonance in Series LRC Circuits(0)
- Power in AC Circuits(0)
- 32. Electromagnetic Waves(0)
- 33. Geometric Optics(0)
- 34. Wave Optics(0)
- 35. Special Relativity(0)
23. The Second Law of Thermodynamics
Heat Engines & PV Diagrams
23. The Second Law of Thermodynamics
Heat Engines & PV Diagrams: Study with Video Lessons, Practice Problems & Examples
23PRACTICE PROBLEM
A spacecraft propulsion system operates using a Brayton cycle with the following processes: (1-2) adiabatic compression, (2-3) isobaric heating, (3-4) adiabatic expansion, and (4-1) isobaric cooling. The gas mixture behaves as an ideal gas with a heat capacity ratio γ=1.4. Derive the expression for the efficiency e of this Brayton cycle in terms of the pressure ratio P2/P1 and γ.
![PV diagram illustrating the Brayton cycle processes for a spacecraft propulsion system.](data:image/png;base64,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)
A spacecraft propulsion system operates using a Brayton cycle with the following processes: (1-2) adiabatic compression, (2-3) isobaric heating, (3-4) adiabatic expansion, and (4-1) isobaric cooling. The gas mixture behaves as an ideal gas with a heat capacity ratio γ=1.4. Derive the expression for the efficiency e of this Brayton cycle in terms of the pressure ratio P2/P1 and γ.