Detailed Notes on Thermodynamic Cycles and Efficiency

Lecture Notes on Thermodynamics

General Overview

• Course Title: Thermodynamics

• Instructor: Dr. A. N. M. Mizanur Rahman

• Course Code: ME 2105

• Credit: 4.0

Thermodynamic Cycles

Definition

• A thermodynamic cycle is a series of processes that return a system to its initial state. In power cycles, heat is continuously converted to work using a working fluid.

Classification of Power Cycles

1. Gas Power Cycles: The working fluid remains in the gaseous phase.

2. Vapor Power Cycles: The working fluid undergoes phase changes, being in both gaseous and liquid phases.

Various Types of Power Cycles

• Gas Power Cycles:

  • Carnot cycle

  • Otto cycle

  • Diesel cycle

  • Brayton cycle

• Vapor Power Cycles:

  • Rankine cycle

  • Reheat cycle

  • Regenerative cycle

  • Stirling cycle

  • Ericsson cycle

Efficiency and Performance Calculations

First Law of Thermodynamics

• The relationship for any cyclic process:
  egin{equation} ag{1} \oint dQ = \oint dW \end{equation}
  Where ( W ) is the work done and ( Q ) is the heat transferred.

Definitions

• Net Work, ( W_{net} ):

  • W{net} = QA - \perspec{|}{Q_R}

• Thermal Efficiency ( e ):

  • $e = \frac{W<em>{net}}{Q</em>A} = \frac{Q<em>A - |Q</em>R|}{Q_A}$

Heat Rate

• Heat Rate defines the amount of heat required per unit work output, leading to efficiencies expressed in hp.hr and kw.hr terms.

• $e = \frac{2544}{\dot{Q<em>A}} \quad \text{(if } Q</em>A ext{ is in hp.hr.)}$

• $e = \frac{3412}{\dot{Q<em>A}} \quad \text{(if } Q</em>A ext{ is in kw.hr.)}$

The Carnot Cycle

Characteristics

• Consists of two isothermal and two adiabatic processes.

• Thermal Efficiency:
  $e = 1 - \frac{T<em>2}{T</em>1}$

• Where, ( T1 ) and ( T2 ) are the temperatures of the hot and cold reservoirs, respectively.

• Work Done:
  $W<em>{net} = (T</em>1 - T_2) \Delta S$

Ideal Gas and Carnot Cycle

Important Relations

• Heat Added and Rejected for an Ideal Gas:

  • $Q<em>A = R T</em>1 \ln \left(\frac{V<em>2}{V</em>1}\right)$

  • $|Q<em>R| = R T</em>2 \ln \left(\frac{V<em>3}{V</em>4}\right)$

Efficiency Calculation

• The efficiency can also be expressed as:
  $e = 1 - \frac{T<em>2}{T</em>1}$

Internal Combustion Engine Cycles

Characteristics

• Involves combustion inside the engine cylinder; classified as non-cyclic due to permanent chemical changes.

Air Standard Cycle Assumptions

• Ideal gas behavior and constant specific heats.

• Otto Cycle Analysis:

  • Total Processes: 4 (2 constant volume and 2 isentropic)

• Efficiency:
  $\eta<em>{otto} = 1 - \frac{T</em>4 - T<em>1}{T</em>3 - T_2}$

Diesel Cycle

Key Features

• Achieved by compressing air and then injecting fuel for combustion.

• Efficiency Expression:
  $\eta<em>{diesel} = 1 - \frac{u</em>4 - u<em>1}{h</em>3 - h_2}$

• Explains the nature of thermal efficiency dependency on cut-off ratios.

Comparison of Otto and Diesel Cycles

• Efficiency: Diesel cycle generally allows higher thermal efficiencies due to the nature of air-only compression.

Brayton Cycle

Description

• Found in gas turbine applications.

• Consists of 2 adiabatic and 2 isobaric processes.

• Efficiency:
  $\eta = 1 - \frac{T<em>4 - T</em>1}{T<em>3 - T</em>2}$

Comparison with Otto Cycle

• For the same compression ratio, efficiencies are comparable but different in operational dynamics.

Regenerator Functionality

• A component that stores heat for thermodynamic reversibility during cycles in engines like Stirling and Ericsson engines.

Final Remarks and Considerations

1. The analysis of thermodynamic cycles is crucial for understanding how engines convert heat to work.

2. Efficiency calculations are heavily reliant on temperature ratios and specific heat definitions.

3. Variations in cycles reflect adaptations in engine technology for efficiency and performance optimization.

Note: For specific formulas or processes, derivations may be done to reflect practical applications in engineering contexts. Ensure to refer back to calculations presented for accuracy in application scenarios.