Overview

This script builds a complete pressure–volume diagram of an ideal Diesel cycle. You see all four processes clearly. The model uses standard air assumptions and basic thermodynamic relations.

You all can generete:

  • Compression curve
  • Heat addition at constant pressure
  • Expansion curve
  • Heat rejection at constant volume

The result matches the classic Diesel cycle diagram used in thermodynamics.

Key Inputs

The model starts with three core parameters:

  • gamma = 1.4
    Ratio of specific heats for air
  • r = 18
    Compression ratio
    Higher value increases peak pressure and efficiency
  • rc = 3
    Cut-off ratio
    Controls how long heat addition continues

These three values shape the entire cycle.

You all can adjust and set the above value as per your requirement and observe the behavior of PV diagram.

State Point Calculations

We can define four thermodynamic states.

State 1

  • Initial condition
  • V1 = 1, P1 = 1
  • Used as reference

State 2

  • End of compression
  • Volume reduces by factor r
  • Pressure rises using isentropic relation

P2=P1⋅rγP_2 = P_1 \cdot r^\gamma

State 3

  • Heat addition at constant pressure
  • Volume increases using cut-off ratio

V3=rc⋅V2V_3 = r_c \cdot V_2

  • Pressure remains constant

State 4

  • Expansion back to original volume
  • Pressure drops using isentropic relation

P4=P3⋅(V3V4)γP_4 = P_3 \cdot \left(\frac{V_3}{V_4}\right)^\gamma

These four points define the full cycle.

Process Modeling

Each process is generated using arrays of points.

1–2 Compression

  • Isentropic process
  • Pressure rises sharply
  • Curve bends steeply
P_12 = P1 * (V1 ./ V_12).^gamma;

2–3 Heat Addition

  • Constant pressure
  • Horizontal line
  • Volume increases

3–4 Expansion

  • Isentropic expansion
  • Pressure drops smoothly
  • Longer curve compared to compression

4–1 Heat Rejection

  • Constant volume
  • Vertical drop in pressure

Plot Construction

The script plots each process with distinct colors:

  • Blue: Compression
  • Red: Heat addition
  • Yellow: Expansion
  • Green: Heat rejection

State points are marked using black filled circles. This improves readability.

plot([V1 V2 V3 V4], [P1 P2 P3 P4], 'ko', 'MarkerFaceColor','k');

The script adds light dashed lines to improve interpretation.

Vertical guides

  • At V2, V3, and V1
  • Show key volume transitions

Horizontal guides

  • At P2, P4, and P1
  • Help compare pressure levels
lineColor = [0.6 0.6 0.6 0.6];

Full code for MATLAB Scripting

clc;
clear;
close all;
% Parameters
gamma = 1.4;          % specific heat ratio
r = 18;               % compression ratio (V1/V2)
rc = 3;               % cut-off ratio (V3/V2)
% State 1
V1 = 1;
P1 = 1;
% State 2 (after isentropic compression)
V2 = V1 / r;
P2 = P1 * r^gamma;
% State 3 (after constant pressure heat addition)
V3 = rc * V2;
P3 = P2;
% State 4 (after isentropic expansion)
V4 = V1;
P4 = P3 * (V3 / V4)^gamma;
% Process curves
% 1-2: isentropic compression
V_12 = linspace(V1, V2, 100);
P_12 = P1 * (V1 ./ V_12).^gamma;
% 2-3: constant pressure
V_23 = linspace(V2, V3, 100);
P_23 = P2 * ones(size(V_23));
% 3-4: isentropic expansion
V_34 = linspace(V3, V4, 100);
P_34 = P3 * (V3 ./ V_34).^gamma;
% 4-1: constant volume
V_41 = V1 * ones(1,100);
P_41 = linspace(P4, P1, 100);
% Plot
figure;
hold on;
plot(V_12, P_12, 'b', 'LineWidth', 2);
plot(V_23, P_23, 'r', 'LineWidth', 2);
plot(V_34, P_34, 'y', 'LineWidth', 2);
plot(V_41, P_41, 'g', 'LineWidth', 2);
% Mark points
plot([V1 V2 V3 V4], [P1 P2 P3 P4], 'ko', 'MarkerFaceColor','k');
% Labels
xlabel('Volume');
ylabel('Pressure');
title('Diesel Cycle P-V Diagram');
grid on;
% Light guide lines (like in your image)
lineColor = [0.6 0.6 0.6 0.6];
% Vertical lines at V2 and V3
plot([V2 V2], [0 P2], '--', 'Color', lineColor, 'LineWidth', 1);
plot([V3 V3], [0 P3], '--', 'Color', lineColor, 'LineWidth', 1);
plot([V1 V1], [0 P4], '--', 'Color', lineColor, 'LineWidth', 1);
% Horizontal lines at P2 and P4
plot([0 V2], [P2 P2], '--', 'Color', lineColor, 'LineWidth', 1);
plot([0 V1], [P4 P4], '--', 'Color', lineColor, 'LineWidth', 1);
plot([0 V1], [P1 P1], '--', 'Color', lineColor, 'LineWidth', 1);
legend('1-2 Compression','2-3 Heat Addition','3-4 Expansion','4-1 Heat Rejection');
hold off;