Part II: Cycles and Fluid Properties · Topic 4 of 8 · 19 min read

Ideal Gas Cycles and Thermal Efficiency

Analyse closed loops, air-standard engine cycles and their performance limits.

What you'll learn

Read a cycle as a closed path of heat and work interactions.
Calculate ideal efficiency and temperature ratios for air-standard cycles.
Distinguish constant-volume and constant-pressure heat addition.
Recognise the limitations of idealised cycle models.

An ideal engine cycle connects compression, heat addition, expansion and heat rejection.

Understand the concepts

Why cycles produce net work

In a cycle, every state property returns to its initial value, so $\Delta U_{cycle}=0$ . The first law therefore gives $W_{net}=Q_{net}$ . On a quasistatic - diagram, the enclosed signed area is net boundary work.

Assumptions and sign conventions

Use a constant heat-capacity ratio when analysing ideal-gas isentropic stages.
Ignore friction and heat leakage when an ideal air-standard cycle is specified.
Define $Q_{out}$ as a positive magnitude in efficiency expressions.

Equations that matter

\eta_{th}=\frac{W_{net}}{Q_{in}}=1-\frac{Q_{out}}{Q_{in}}

Step-by-step method

Identify the sequence and type of each process on the cycle diagram.
Calculate intermediate temperatures using isentropic and heat-addition relations.
Compute the heat received and rejected using the correct specific heat.
Calculate net work and thermal efficiency.
Check that cyclic energy conservation holds and that efficiency lies between zero and one.

Worked example: Compression ratio and ideal efficiency

An ideal constant-volume heat-addition cycle uses $r=8.5$ and $\gamma=1.4$ . Determine its ideal thermal efficiency and the ideal post-compression temperature when the intake temperature is $300\,\mathrm{K}$ .

An ideal compression cycle has four labelled states and a specified compression ratio.

Step 1: Efficiency from the compression ratio
Apply the ideal cycle expression.
$\eta_{th}=1-8.5^{-0.4}=0.5752$

Common mistakes

Confusing a pressure ratio with a volume compression ratio.
Using $c_p$ for a constant-volume heat-input stage.
Forgetting to use Kelvin in temperature ratios.
Treating ideal efficiency as guaranteed actual engine efficiency.

Check yourself

Why is the enclosed $P$ - $V$ loop area equal to net work?
What happens to ideal efficiency as compression ratio rises?
How does constant-pressure heat addition differ from constant-volume heat addition?

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Try Practice Questions (4)

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Ideal Gas Cycles and Thermal Efficiency

What you'll learn

Understand the concepts

Why cycles produce net work

Assumptions and sign conventions

Equations that matter

Step-by-step method

Worked example: Compression ratio and ideal efficiency

Step 1: Efficiency from the compression ratio

Common mistakes

Check yourself

Thermal efficiency

Isentropic ideal-gas compression

Constant-volume heat addition

Constant-pressure heat addition

Cycle models versus actual machines

Step 2: Isentropic compression temperature