Applied Thermodynamics Cheat Sheet

This cheat sheet covers fundamental concepts and derivations in applied thermodynamics, focusing on cycles, compressors, nozzles, and psychrometrics, essential for mechanical engineering studies.

Core Principles

Understanding of thermodynamic cycles (Rankine, Brayton, Otto, Diesel, Dual).
Analysis of refrigeration and psychrometric processes.
Derivations for thermal efficiency and work in various systems.
Principles of compressible flow through nozzles and shock waves.
Compressor performance and efficiency factors.

Action Steps

Define stoichiometric air-fuel ratio.
Derive adiabatic flame temperature expression.
Draw and explain Rankine cycle with reheat and regeneration.
Compare Otto, Diesel, and Dual cycles with diagrams.
Explain Brayton cycle with regeneration, intercooling, and reheating.
Explain vapor compression refrigeration cycle with P-H and T-S diagrams.
Define DBT, WBT, dew point, and relative humidity.
Explain psychrometric processes using a psychrometric chart.
Define stagnation properties.
Derive condition for choked flow in a convergent nozzle.
Explain normal shock waves and derive relations.
Derive minimum work for multistage compressor with intercooling.
Explain effect of clearance volume on volumetric efficiency.
Explain velocity and pressure compounding.
Calculate thermal efficiency of a Rankine cycle.
Calculate theoretical air requirement and excess air.
Determine Mach number and critical pressure ratio for isentropic flow.

Formulas

Thermal efficiency of Rankine cycle: $\eta = 1 - \frac{Q_{out}}{Q_{in}}$
Thermal efficiency of Brayton cycle: $\eta = 1 - \frac{T_1}{T_2}$
Thermal efficiency of Otto cycle: $\eta = 1 - \frac{1}{r^{\gamma-1}}$
Thermal efficiency of Diesel cycle: $\eta = 1 - \frac{1}{\gamma} \frac{r_c^{\gamma}-1}{r_c-1} \frac{1}{r^{\gamma-1}}$
Condition for choked flow in a convergent nozzle: $M = 1$
Critical pressure ratio for isentropic flow: $\frac{P_0}{P^*} = \left(1 + \frac{\gamma-1}{2} M^{*2}\right)^{\frac{\gamma}{\gamma-1}}$

Key Terms

Stoichiometric Air-Fuel Ratio: The ideal air-fuel ratio where complete combustion occurs, with no excess air or unburnt fuel.
Adiabatic Flame Temperature: The theoretical maximum temperature reached during combustion assuming no heat loss.
Rankine Cycle: A thermodynamic cycle that converts heat into work, typically used in steam power plants.
Brayton Cycle: A thermodynamic cycle that describes the workings of gas turbine engines.
Psychrometrics: The study of the thermal properties of moist air and the processes that affect them.
Choked Flow: The condition in fluid flow where the velocity reaches the speed of sound (Mach 1) at the narrowest point (throat).
Normal Shock Wave: A shock wave that stands perpendicular to the direction of fluid flow.
Volumetric Efficiency: The ratio of the actual volume of fluid drawn into a compressor cylinder to the total volume of the cylinder.

Pro Tips

Always use neat, labeled diagrams for cycle explanations.
Clearly state assumptions made during derivations.
Pay attention to units in numerical problems.
Relate theoretical concepts to practical applications.
Understand the impact of each process (reheat, intercooling) on efficiency.

Pitfalls to Avoid

Confusing different thermodynamic cycles.
Incorrectly applying formulas for efficiency.
Errors in P-V and T-S diagram interpretations.
Forgetting to account for clearance volume in compressors.
Misinterpreting shock wave phenomena.
Calculation errors in numerical problems.

People

Curtis: Associated with velocity compounding in turbine stages.
Rateau: Associated with pressure compounding in turbine stages.