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Qwestrum Engineering360 · Mechanical Engineering · Thermodynamics

Thermodynamic Cycles

A power cycle's thermal efficiency is η = W_net/Q_in = 1 − Q_out/Q_in; the net work equals the enclosed area on both the P–v and T–s diagrams. Clockwise cycles are engines, anticlockwise are refrigerators, per P.K. Nag.
Exam tip: lock the sign convention (Q into system, W by system in P.K. Nag) before substituting; use absolute temperature for ideal-gas and efficiency ratios.

Key formulas & points

Skim these first — then read the full notes below.

  • Clockwise cycle on T-s: heat engine; anticlockwise: refrigerator
  • Backworkratio=WcompWturbineBack work ratio = \frac{W_{comp}}{W_{turbine}} (gas cycles)
  • Regeneration improves efficiency by preheating feedwater/burner air

Topic details

Introduction

Thermodynamic cycles tie together the first and second laws and set up the specialised power and refrigeration cycles studied later. P.K. Nag treats each cycle as a sequence of processes and evaluates heat and work process by process.

Scope in B.Tech and GATE syllabus

The universal result is that net work equals net heat over a cycle (ΔU = 0), so η = W_net/Q_in = 1 − Q_out/Q_in. On a T–s diagram the enclosed area is the net heat and hence the net work — a powerful visual check.

Why this topic matters in practice

Improvements — regeneration, reheat, intercooling — all aim to raise the mean temperature of heat addition or lower that of rejection, pushing efficiency toward the Carnot bound. Indian exams reward students who trace every process on P–v and T–s before computing η, because the diagram reveals sign and area errors immediately.

Key relations & formulas

η=WnetQin=1−QoutQin\eta = \frac{W_{net}}{Q_{in}} = 1 - \frac{Q_{out}}{Q_{in}}
(cycle thermal efficiency)

Formulas (Indian textbook notation)

  • Wnet=∮δW=areaonP−vdiagramW_{net} = ∮ \delta W = area on P-v diagram

Formulas (Indian textbook notation)

  • Qnet=∮δQ=areaonT−sdiagramQ_{net} = ∮ \delta Q = area on T-s diagram

Formulas (Indian textbook notation)

  • mcpΔTforsensibleheat;m⋅hfgforphasechangemcp\Delta T for sensible heat; m\cdot h_{fg} for phase change

Notation and sign conventions

Relation 1 —
η=WnetQin=1−QoutQin\eta = \frac{W_{net}}{Q_{in}} = 1 - \frac{Q_{out}}{Q_{in}}
η=WnetQin=1−QoutQin\eta = \frac{W_{net}}{Q_{in}} = 1 - \frac{Q_{out}}{Q_{in}}
(cycle thermal efficiency)
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
Wnet=∮δW=areaonP−vdiagramW_{net} = ∮ \delta W = area on P-v diagram

Formulas (Indian textbook notation)

  • Wnet=∮δW=areaonP−vdiagramW_{net} = ∮ \delta W = area on P-v diagram
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
Qnet=∮δQ=areaonT−sdiagramQ_{net} = ∮ \delta Q = area on T-s diagram

Formulas (Indian textbook notation)

  • Qnet=∮δQ=areaonT−sdiagramQ_{net} = ∮ \delta Q = area on T-s diagram
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 4 —
mcpΔTforsensibleheat;m⋅hfgforphasechangemcp\Delta T for sensible heat; m\cdot h_{fg} for phase change

Formulas (Indian textbook notation)

  • mcpΔTforsensibleheat;m⋅hfgforphasechangemcp\Delta T for sensible heat; m\cdot h_{fg} for phase change
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Fundamentals and definitions

Over any cycle internal energy returns to its start, so ∮dU = 0 and W_net = Q_net = Q_in − Q_out. Thermal efficiency is therefore η = 1 − Q_out/Q_in, bounded above by the Carnot value 1 − T_L/T_H.

Governing relations in practice

On a P–v diagram the enclosed area is the net work; on a T–s diagram it is the net heat, which equals net work. A clockwise loop delivers positive work (engine); an anticlockwise loop consumes work to pump heat (refrigerator/heat pump).

Design and analysis considerations

For gas cycles the back-work ratio W_comp/W_turbine indicates how much turbine output is consumed compressing the working fluid; it is high for gas turbines and low for steam cycles because pumping a liquid costs little.

Advanced theory and extensions

Efficiency is raised by increasing the average temperature of heat addition (superheat, reheat) or decreasing that of rejection (lower condenser pressure), and by regeneration that internally recovers heat. These strategies, plus careful process-by-process accounting, define cycle analysis.

Assumptions and validity limits

State assumptions explicitly before using any relation for thermodynamic cycles — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Thermodynamics viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Thermodynamics papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to thermodynamic cycles.
4. Use equation 1:
η=WnetQin=1−QoutQin\eta = \frac{W_{net}}{Q_{in}} = 1 - \frac{Q_{out}}{Q_{in}}
.
5. Use equation 2:
Wnet=∮δW=areaonP−vdiagramW_{net} = ∮ \delta W = area on P-v diagram
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Thermodynamic Cycles appears in engines, boilers, and refrigeration cycles. In Indian mechanical curricula this topic is tested because it connects theory to energy, heat, and work in thermal systems.
GATE and semester exams often combine thermodynamic cycles with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use thermodynamic cycles?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

• Forgetting that net work equals the enclosed area only when the cycle is traced consistently
• Mixing up Q_in and Q_out signs, giving efficiency greater than one
• Assuming any real cycle can reach Carnot efficiency
• Not distinguishing engine (clockwise) from refrigerator (anticlockwise) loops

Quick revision checklist

Before attempting thermodynamic cycles problems, confirm you can:
1. Clockwise cycle on T-s: heat engine; anticlockwise: refrigerator
2.
Backworkratio=WcompWturbineBack work ratio = \frac{W_{comp}}{W_{turbine}}
(gas cycles)
3. Regeneration improves efficiency by preheating feedwater/burner air
Revise the solved examples in Engineering Thermodynamics — P.K. Nag and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Cycle thermal efficiency

Problem

A power cycle receives Q_in = 1000 kJ and rejects Q_out = 600 kJ per cycle. Find the net work and thermal efficiency.

Solution

W_net = Q_in − Q_out = 1000 − 600 = 400 kJ; η = W_net/Q_in = 400/1000 = 0.40 (40 %).

Conceptual check — Thermodynamic Cycles

Problem

In a Thermodynamics semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of thermodynamic cycles." What should a complete answer include?

Practice questions

Most-asked interview and GATE questions for this topic — expand any item for a model answer.

  1. 1
    What is Thermodynamic Cycles, and why does it appear in B.Tech / GATE syllabi?

    Model answer

    A power cycle's thermal efficiency is η = W_net/Q_in = 1 − Q_out/Q_in; the net work equals the enclosed area on both the P–v and T–s diagrams. Clockwise cycles are engines, anticlockwise are refrigerators, per P.K. Nag.
  2. 2
    State the relation η = W_net/Q_in = 1 − Q_out/Q_in and name each symbol.

    Model answer

    The governing relation is η=WnetQin=1−QoutQin\eta = \frac{W_{net}}{Q_{in}} = 1 - \frac{Q_{out}}{Q_{in}}. Write every symbol with SI units before substituting numbers.
  3. 3
    State the relation W_net = ∮ δW = area on P-v diagram and name each symbol.

    Model answer

    The governing relation is Wnet=∮δW=areaonP−vdiagramW_{net} = ∮ \delta W = area on P-v diagram. Write every symbol with SI units before substituting numbers.
  4. 4
    State the relation Q_net = ∮ δQ = area on T-s diagram and name each symbol.

    Model answer

    The governing relation is Qnet=∮δQ=areaonT−sdiagramQ_{net} = ∮ \delta Q = area on T-s diagram. Write every symbol with SI units before substituting numbers.
  5. 5
    State the relation mcpΔT for sensible heat; m·h_fg for phase change and name each symbol.

    Model answer

    The governing relation is mcpΔTforsensibleheat;m⋅hfgforphasechangemcp\Delta T for sensible heat; m\cdot h_{fg} for phase change. Write every symbol with SI units before substituting numbers.
  6. 6
    Explain: Clockwise cycle on T-s: heat engine; anticlockwise: refrigerator

    Model answer

    Clockwise cycle on T-s: heat engine; anticlockwise: refrigerator — state the assumption range and one exam trap linked to this point.
  7. 7
    Explain: Back work ratio = W_comp/W_turbine (gas cycles)

    Model answer

    Backworkratio=WcompWturbineBack work ratio = \frac{W_{comp}}{W_{turbine}} (gas cycles) — state the assumption range and one exam trap linked to this point.
  8. 8
    Explain: Regeneration improves efficiency by preheating feedwater/burner air

    Model answer

    Regeneration improves efficiency by preheating feedwater/burner air — state the assumption range and one exam trap linked to this point.
  9. 9
    How would you correct this error in a viva: Forgetting that net work equals the enclosed area only when the cycle is traced consistently?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  10. 10
    How would you correct this error in a viva: Mixing up Q_in and Q_out signs, giving efficiency greater than one?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  11. 11
    How would you correct this error in a viva: Assuming any real cycle can reach Carnot efficiency?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  12. 12
    How would you correct this error in a viva: Not distinguishing engine (clockwise) from refrigerator (anticlockwise) loops?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.

Exams & GATE

  • 1
    P.K. Nag Ch. 8–10 — trace each process on P-v and T-s before calculating η.
  • 2
    Avoid: Forgetting that net work equals the enclosed area only when the cycle is traced consistently
  • 3
    Avoid: Mixing up Q_in and Q_out signs, giving efficiency greater than one
  • 4
    Avoid: Assuming any real cycle can reach Carnot efficiency

📖 Standard books (India)

  • Engineering Thermodynamics — P.K. Nag

    Read: Syllabus unit

    The standard thermodynamics text in most Indian universities

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