Principles and Practice of Engineering Exam (PE) Mechanical Engineering (PE Mechanical) Syllabus

Mechanical Engineering (PE Mechanical) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mechanical Engineering (PE Mechanical) in Principles and Practice of Engineering Exam (PE), not a summary of it.

1. 1

   Thermodynamics and Energy Systems

   3 topics

   • Laws of Thermodynamics
     • First and second law applications
     • Entropy and availability
     • Property tables and ideal gas behavior
   • Power Cycles
     • Rankine and Brayton cycles
     • Reheat and regeneration
     • Combustion and efficiency
   • Refrigeration and HVAC Cycles
     • Vapor-compression refrigeration
     • Psychrometrics and air conditioning processes
     • Heating and cooling load calculations
2. 2

   Fluid Mechanics and Heat Transfer

   3 topics

   • Fluid Statics and Dynamics
     • Bernoulli and energy equations
     • Pipe flow, friction, and minor losses
     • Pumps, fans, and affinity laws
   • Heat Transfer Modes
     • Conduction and thermal resistance
     • Convection correlations
     • Radiation exchange
   • Heat Exchangers
     • LMTD and effectiveness-NTU methods
     • Fouling and configuration
3. 3

   Machine Design and Materials

   3 topics

   • Stress Analysis
     • Combined and principal stresses
     • Mohr's circle and failure theories
     • Fatigue and stress concentration
   • Machine Components
     • Shafts, keys, and couplings
     • Bearings, gears, and belts
     • Bolted and welded joints
   • Engineering Materials
     • Material properties and selection
     • Heat treatment and failure modes
4. 4

   Mechanical Systems and Controls

   3 topics

   • Dynamics and Vibration
     • Kinematics and kinetics of bodies
     • Free and forced vibration
     • Natural frequency and resonance
   • Measurement and Instrumentation
     • Sensors and transducers
     • Calibration and uncertainty
   • Control Systems
     • Feedback and block diagrams
     • PID control and stability

Mechanical Engineering (PE Mechanical) flashcards for Principles and Practice of Engineering Exam (PE)

18 of 62 cards from the Mechanical Engineering (PE Mechanical) deck — real questions with worked answers.

1. State the First Law of Thermodynamics for a closed system in differential form, and define each term.

   $$dU = \delta Q - \delta W$$ The change in internal energy $dU$ equals heat added to the system $\delta Q$ minus work done by the system $\delta W$. It is a statement of energy conservation.

2. What does the Second Law of Thermodynamics state in terms of entropy for an isolated system?

   The total entropy of an isolated system can never decrease: $$\Delta S_{\text{universe}} \geq 0$$ Equality holds only for reversible processes; real (irreversible) processes generate entropy.

3. Write the steady-flow energy equation (SFEE) for a single-inlet, single-outlet open system.

   $$\dot{Q} - \dot{W} = \dot{m}\left[(h_2 - h_1) + \frac{V_2^{2} - V_1^{2}}{2} + g(z_2 - z_1)\right]$$ where $h$ is specific enthalpy, $V$ velocity, and $z$ elevation.

4. Define the Zeroth Law of Thermodynamics.

   If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This law establishes temperature as a measurable property.

5. What is the Carnot efficiency of a heat engine operating between hot and cold reservoirs, and what does it represent?

   $$\eta_{\text{Carnot}} = 1 - \frac{T_C}{T_H}$$ with $T_C, T_H$ in absolute (Kelvin) units. It is the maximum possible thermal efficiency for any heat engine operating between those two temperatures.

6. Define entropy change for a reversible process and give the relation involving heat.

   $$dS = \frac{\delta Q_{\text{rev}}}{T}$$ Entropy is a property; its change between two states is path-independent and equals the integral of reversible heat transfer divided by absolute temperature.

7. What is the thermal efficiency of an ideal Carnot (or any) heat engine in terms of heat flows?

   $$\eta_{th} = \frac{W_{net}}{Q_H} = 1 - \frac{Q_C}{Q_H}$$ where $Q_H$ is heat in from the hot reservoir and $Q_C$ is heat rejected to the cold reservoir.

8. List the four processes of the ideal Otto cycle in order.

   1) Isentropic compression; 2) Constant-volume heat addition; 3) Isentropic expansion (power stroke); 4) Constant-volume heat rejection. It models the spark-ignition (gasoline) engine.

9. Give the thermal efficiency of the ideal Otto cycle in terms of compression ratio $r$ and specific heat ratio $k$.

   $$\eta_{Otto} = 1 - \frac{1}{r^{k-1}}$$ where $r = V_1/V_2$ is the compression ratio and $k = c_p/c_v$.

10. How does the ideal Diesel cycle differ from the Otto cycle, and what is its efficiency expression?

    The Diesel cycle uses constant-pressure (rather than constant-volume) heat addition. $$\eta_{Diesel} = 1 - \frac{1}{r^{k-1}}\left[\frac{r_c^{k}-1}{k(r_c-1)}\right]$$ where $r_c$ is the cutoff ratio. For equal $r$, Otto is more efficient than Diesel.

11. List the four ideal components/processes of the Rankine cycle (steam power plant).

    1) Pump: isentropic compression of liquid; 2) Boiler: constant-pressure heat addition; 3) Turbine: isentropic expansion; 4) Condenser: constant-pressure heat rejection.

12. Write the back-work ratio and pump work expression for a Rankine cycle.

    Pump work (incompressible liquid): $$w_{pump} = v(P_2 - P_1)$$ Back-work ratio $= w_{pump}/w_{turbine}$, which is very small for Rankine cycles (unlike gas-turbine Brayton cycles where it is large).

13. List the components of the ideal Brayton cycle and its efficiency in terms of pressure ratio.

    Components: compressor, combustor (constant-$P$ heat add), turbine, heat rejection. $$\eta_{Brayton} = 1 - \frac{1}{r_p^{(k-1)/k}}$$ where $r_p = P_2/P_1$ is the pressure ratio. Models gas turbines/jet engines.

14. What is the purpose of regeneration, reheat, and intercooling in power cycles?

    Regeneration: preheat feedwater/air with extracted heat to raise efficiency. Reheat: re-expand after intermediate reheating to increase work and avoid excess moisture. Intercooling: cool gas between compressor stages to reduce compression work.

15. Define the Coefficient of Performance (COP) for a refrigeration cycle and for a heat pump.

    Refrigerator: $$COP_R = \frac{Q_C}{W_{net}} = \frac{Q_C}{Q_H - Q_C}$$ Heat pump: $$COP_{HP} = \frac{Q_H}{W_{net}} = COP_R + 1$$

16. List the four components of the ideal vapor-compression refrigeration cycle in order.

    1) Compressor (isentropic, raises P & T of vapor); 2) Condenser (rejects heat, condenses to liquid); 3) Expansion/throttling valve (isenthalpic pressure drop); 4) Evaporator (absorbs heat, vaporizes refrigerant).

17. What type of process occurs across the throttling valve in a refrigeration cycle, and what property is conserved?

    An isenthalpic (constant-enthalpy) throttling process: $$h_{in} = h_{out}$$ It is irreversible, with a large entropy increase and a pressure/temperature drop, but no work or heat transfer.

18. Define the ton of refrigeration in SI and US units.

    1 ton of refrigeration = rate of heat removal to freeze 1 short ton of water (0 to ice) in 24 hours $\approx 12{,}000\ \text{Btu/hr} = 3.517\ \text{kW}$.

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