Thermodynamic Cycles: Introduction and Analysis

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Questions and Answers

What is a thermodynamic cycle?

A sequence of processes that begins and ends at the same state.

In a thermodynamic cycle, the system experiences a net change of state.

False (B)

What happens to all properties at the conclusion of a thermodynamic cycle?

All properties have the same values they had at the beginning.

What are devices or systems used to produce a net power output often called?

<p>Engines</p> Signup and view all the answers

What are thermodynamic cycles that engines operate on called?

<p>Power cycles</p> Signup and view all the answers

What is the purpose of heat engines?

<p>Converting thermal energy to work</p> Signup and view all the answers

What are devices or systems used to produce refrigeration called?

<p>All of the above (D)</p> Signup and view all the answers

What is the objective of a refrigeration cycle?

<p>Cool a refrigerated space or to maintain the temperature below that of the surroundings.</p> Signup and view all the answers

What is the objective of a heat pump?

<p>Maintain the temperature above that of the surroundings.</p> Signup and view all the answers

What does COP stand for?

<p>Coefficient of Performance</p> Signup and view all the answers

The net work of a power cycle operating is 10,000 kJ, and the thermal efficiency is 0.4. Determine the heat transfer $Q_{in}$ in kJ.

<p>25000 kJ</p> Signup and view all the answers

A refrigeration cycle operating has $Q_{out}$ = 1000 Btu and $W_{cycle}$ = 300 Btu. Determine the coefficient of performance for the cycle.

<p>2.33</p> Signup and view all the answers

A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes in series. Determine the volume at state 1 in m3, if the volume at state 3 is 0.028 m3 and the work is -8.3 kJ.

<p>0.103 m³</p> Signup and view all the answers

A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes in series. Determine the work for process 1-2, each in kJ, if the volume at state 3 is 0.028 m3 and the work is -8.3 kJ.

<p>-18.8 kJ</p> Signup and view all the answers

A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes in series. Determine the heat transfer for process 1-2, each in kJ, if the volume at state 3 is 0.028 m3 and the work is -8.3 kJ.

<p>-18.8 kJ</p> Signup and view all the answers

A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes in series. Can this be a power cycle or a refrigeration cycle?

<p>Refrigeration Cycle (B)</p> Signup and view all the answers

A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes in series, beginning at state 1 where $p_1$ = 1 bar, $V_1= 1.5 m^3$, as follows: Process 1-2: Compression with $pV = constant, W_{12} = -104 kJ, U_1 = 512 kJ, U_2 = 690 kJ$. Process 2-3: $W_{23} = 0, Q_{23} = -150 kJ$. Process 3-1: $W_{31} = +50 kJ$. Determine $Q_{12}$ in kJ.

<p>74 kJ</p> Signup and view all the answers

A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes in series, beginning at state 1 where $p_1$ = 1 bar, $V_1= 1.5 m^3$, as follows: Process 1-2: Compression with $pV = constant, W_{12} = -104 kJ, U_1 = 512 kJ, U_2 = 690 kJ$. Process 2-3: $W_{23} = 0, Q_{23} = -150 kJ$. Process 3-1: $W_{31} = +50 kJ$. Is this a power cycle? Explain.

<p>Reversed Cycle (A)</p> Signup and view all the answers

A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes: Process 1-2: Compression with $pV = constant$, from $p_1$ = 1 bar, $V_1 = 2 m^3$ to $V_2 = 0.2 m^3$, $U_2 - U_1 = 100 kJ$. Process 2-3: Constant volume to $p_3$ = $p_1$. Process 3-1: Constant-pressure and adiabatic process. Determine the net work of the cycle, in kJ.

<p>-280.52 kJ</p> Signup and view all the answers

A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes: Process 1-2: Compression with $pV = constant$, from $p_1$ = 1 bar, $V_1 = 2 m^3$ to $V_2 = 0.2 m^3$, $U_2 - U_1 = 100 kJ$. Process 2-3: Constant volume to $p_3$ = $p_1$. Process 3-1: Constant-pressure and adiabatic process. Determine the heat transfer for process 2-3, in kJ.

<p>80kJ</p> Signup and view all the answers

A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes: Process 1-2: Compression with $pV = constant$, from $p_1$ = 1 bar, $V_1 = 2 m^3$ to $V_2 = 0.2 m^3$, $U_2 - U_1 = 100 kJ$. Process 2-3: Constant volume to $p_3$ = $p_1$. Process 3-1: Constant-pressure and adiabatic process. Is this a power cycle or a refrigeration cycle?

<p>Refrigeration Cycle (A)</p> Signup and view all the answers

Flashcards

Thermodynamic Cycle

A sequence of processes that begins and ends at the same state.

Cycle State Change

Over a complete cycle, the system experiences no net change of state; all properties return to their initial values.

Cycle Energy Balance Equation

∆𝐸𝐶𝑦𝑐𝑙𝑒 = 𝑄𝐶𝑦𝑐𝑙𝑒 − 𝑊𝐶𝑦𝑐𝑙𝑒. Represents the energy balance of the cycle.

𝑾𝑪𝒚𝒄𝒍𝒆 = 𝑸𝑪𝒚𝒄𝒍𝒆

The net work done by the cycle is equal to the net heat transfer during the cycle.

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Power Cycles

Cycles designed to produce a net power output.

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Thermal Efficiency (ηth)

The ratio of the desired output (net work) to the required input (heat added).

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Refrigeration Cycles

Cycles designed to transfer heat from a cold reservoir to a hot reservoir, requiring work input.

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Refrigeration Cycle Objective

A reversed cycle where the objective is to cool a refrigerated space.

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Heat Pump Objective

A reversed cycle where the objective is to maintain the temperature above that of the surroundings.

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Coefficient of Performance (COP)

Measures the efficiency of a refrigeration cycle. Desired output divided by required input.

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COP (Refrigeration)

The desired output (cooling effect) divided by the required input (work).

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COP (Heat Pump)

The desired output (heating effect) divided by the required input (work).

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Qin

Heat is added to the system.

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Qout

Heat is rejected from the system.

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Power Cycle Purpose

Cycles that produce net work output from heat input.

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Refrigeration Cycle Purpose

Cycles that require work input to transfer heat.

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Heat Engine Cycle

A cycle where thermal energy is converted to work.

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Example cycle processes

Compression, constant-volume cooling, constant-pressure expansion.

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Process: U2 = U1

U2 = U1 occurs in this process

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Process: Constant-volume cooling

Volume is constant with pressure and volume defined

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Process: Constant-pressure Expansion

Pressure is constant with work defined.

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Wcycle = -8.3 kJ; Refrigeration Cycle

This answer indicates the cycle type

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Refrigeration cycle

When the net work is negative.

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Vapor Compression Refrigeration Cycle

Common type of refrigeration cycle involving phase changes of a refrigerant.

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Heat Transfer (Q)

The transfer of energy as heat across the system boundary during a process.

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Work Transfer (W)

The energy transferred when a force acts through a distance; for example, expansion or compression of a gas.

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Internal Energy (U)

The energy stored within a system due to the kinetic and potential energies of its molecules.

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Heat transfer example

U3 = 540 kJ and heat is positive.

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Wnet = -280.52 kJ

Net value is negative.

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Q23 = 80kJ

Positive heat value

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Study Notes

  • Thermodynamic Cycles: Introduction and Analysis by Joseph Aldrin Chua

Thermodynamic Cycle

  • A thermodynamic cycle is a sequence of processes that starts and ends at the same state.
  • At the end of a cycle, all properties have the same values they had at the beginning.
  • The system experiences no net change of state over the cycle.
  • Cycles that are repeated periodically are prominent in many applications.

Cycle Energy Balance

  • ΔEcycle = Qcycle - Wcycle
  • No net change of state implies ΔEcycle = 0.
  • Therefore, Wcycle = Qcycle.
  • In analyzing cycles, energy transfers are normally taken as positive based on the directions of arrows on a sketch of the system, and the energy balance is written accordingly.

Power Cycles

  • Devices or systems producing net power output are called engines.
  • Thermodynamic cycles that engines operate on are power cycles.
  • Heat engines convert thermal energy to work.
  • Performance is expressed via thermal efficiency ηth, where:
  • η = Wcycle / Qin
  • Wcycle = Qin - Qout

Examples of Power Cycles: Otto Cycle

  • Illustration of actual four-stroke spark-ignition engine and ideal Otto cycle is included.

Examples of Power Cycles: Diesel Cycle

  • Diagram of P-v included
  • Spark plug and fuel injector included

Refrigeration Cycles (Reversed cycles)

  • Devices or systems used to produce refrigeration are refrigerators, air conditioners, or heat pumps.
  • The cycles they operate on are refrigeration cycles (reversed cycles).
  • The objective of a refrigeration cycle is to cool a refrigerated space to maintain a temperature below that of the surroundings.
  • The objective of a heat pump is to maintain the temperature above that of the surroundings.
  • Equation for refrigeration and heat pump: Wcycle = Qout - Qin
  • Defining the Coefficient of Performance (COP):
    • β = Qin / Wcycle (refrigeration cycle)
    • γ = Qout / Wcycle (heat pump cycle)

Vapor Compression Refrigeration Cycle

  • Illustration of diagram included
  • Illustration of refrigeration cycle included

Examples

  • Net work of a power cycle is 10,000 kJ, thermal efficiency is 0.4.
    • The heat transfers are: Qin = 25000 kJ; Qout = 15000 kJ.
  • A refrigeration cycle has Qout = 1000 Btu and Wcycle = 300 Btu.
  • The coefficient of performance is: COP = 2.33

Example 3

  • A gas in a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes in series:
  • Process 1-2: Compression with U₂ = U₁.
  • Process 2-3: Constant-volume cooling to p3 = 140 kPa, V₃ = 0.028 m3.
  • Process 3-1: Constant-pressure expansion with W31 = 10.5 kJ.
  • Analysis:
  • Wcycle = -8.3 kJ
  • There are no changes in kinetic or potential energy.
  • It is a refrigeration cycle.
  • Answers: V1 = 0.103 m³; W12 = -18.8 kJ; Q12 = -18.8 kJ

Exercises

  • Exercise 2.77: A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes in series.
  • Process 1-2: Compression with PV = constant, W12 = -104 kJ, U₁ = 512 kJ, U₂ = 690 kJ.
  • Process 2-3: W23 = 0, Q23 = -150 kJ.
  • Process 3-1: W31 = +50 kJ.
  • It is a Reversed Cycle.
  • Answers: Q12 = 74 kJ; Q31 = 22kJ; U3 = 540 kJ
  • Exercise 2.78: A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes.
  • Process 1-2: Compression with PV = constant, from p₁ = 1 bar, V₁ = 2 m³ to V₂ = 0.2 m³, U₂ - U₁ = 100 kJ.
  • Process 2-3: Constant volume to p3 = p1.
  • Process 3-1: Constant-pressure and adiabatic process.
  • Answers: Wnet = -280.52 kJ ; Q23 = 80kJ

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