Uploaded October 2016 | Updated September 2026, 2 weeks ago
In this video we will derive two forms of the combined first and second laws of thermodynamics (energy and enthalpy forms).
We will start with a statement of the first law, then move to a statement of the second law. then define the reversible heat addition and reversible work done on the system, and finally solve for the combined law (energy form). Then we will use the definition of enthalpy to derive the combined law in terms of enthalpy.
In this video we will derive two forms of the combined first and second laws of thermodynamics (energy and enthalpy forms).
We will start with a statement of the first law, then move to a statement of the second law. then define the reversible heat addition and reversible work done on the system, and finally solve for the combined law (energy form). Then we will use the definition of enthalpy to derive the combined law in terms of enthalpy.

![Explained: Popup Menu GUI [MATLAB]
Pop-up menus can be used to make a selection from a list of items. This video shows how to get the users input from a pop-up menu in a MATLAB GUI.
Tip:
The method described in the video gives you a little bit more information to work with when extracting data from the popup menu, but if you want the most efficient code, you can use the code below.
popVal = get(hObject,Value);
assignin(base,popVal,popVal);
In this code, youre simply getting the selected value. The first choice is 1, the second choice is 2, and so on. You can then immediately assign this variable back into the base workspace. This code is much simpler, but you also wont have a variable with the strings of all the choices available. In most of my applications, I dont care about the actual strings, just about the value thats selected. Explained: Popup Menu GUI [MATLAB]](https://i.ytimg.com/vi/Wv6aSJ6ifaQ/mqdefault.jpg)
![Explained: Check Box GUI [MATLAB]
A check box can be used for selection or deselection of an option. This video describes how to get the status of a check box in a MATLAB GUI.
Download the code from my website:
http://goo.gl/jSWqAH Explained: Check Box GUI [MATLAB]](https://i.ytimg.com/vi/XUdhhLyJHBg/mqdefault.jpg)

![Afterburners: Why the Nozzle Opens Wider with Afterburner On
In this video Ill go through an example showing why the nozzle on a jet engine needs to open up wider when the afterburner is on. You can tell that an afterburner is on when you see the visible radiation in the afterburner/jet pipe.
Ill be making some more in-depth videos about converging nozzles, converging-diverging nozzles, nozzle flow, choked flow, etc. If you havent already, subscribe so you can be notified when I post them!
NOTES
► Quick note regarding flow choking: You can increase the mass flow rate even when the flow is choked by increasing the upstream stagnation pressure. When I said you couldnt increase the mass flow rate anymore, it was for a fixed stagnation pressure, because thats what you usually have coming out of the turbine of the engine. So that plot on the board is valid for a fixed P_0, when we keep decreasing P.
REFERENCE VIDEOS
→ Turbojet Thrust Equation:
https://goo.gl/gyaalq
→ Stagnation Relations:
https://goo.gl/yOSNeL
→ Isentropic Relations:
https://goo.gl/vxhrLH
→ Speed of Sound:
https://goo.gl/3qZhII
ASSUMPTIONS AND NOTES
1) The nozzle is isentropic.
- Adiabatic: no heat is added or removed.
- Reversible: no friction, shocks, etc.
2) The working fluid is air. Of course the actual working fluid will be the mixture of air and combustion products. This assumption avoids extra calculations that can certainly be done, but are unnecessary for the outcome of this example.
3) The air is a calorically perfect gas (specific heats are constant).
4) The engine is fitted with a converging nozzle (not converging-diverging).
5) The direct result of turning the afterburner on results in an increase in the stagnation temperature of the fluid.
6) The flow is steady through the nozzle.
7) The flow is quasi-1D.
8) Mass flow rate and stagnation pressure do not change when the afterburner is turned on.
9) Values used are just characteristic numbers that might be valid for real engines.
10) If you do have a converging-diverging nozzle, then to get supersonic flow (higher exit velocities), you will still need to have choked flow. In order to increase subsonic flow to supersonic flow in a CD nozzle, the nozzle must be choked.
THUMBNAIL IMAGE
Photo: SAC Ben Stevenson/MOD [OGL http://www.nationalarchives.gov.uk/doc/open-government-licence/version/1/)], via Wikimedia Commons Afterburners: Why the Nozzle Opens Wider with Afterburner On](https://i.ytimg.com/vi/YKCqyaYMSs8/mqdefault.jpg)




![Explained: Nozzle Mass Flow Rate
One of the important variables in determining how much thrust a rocket can produce is the mass flow rate. In this video, we will derive an expression for the mass flow rate through a converging or converging diverging nozzle.
NOTES
► This expression only works when the flow is choked. For a converging-diverging (CD) nozzle, the flow should always be choked (although you still need to check). A little more care is needed when using the expression for a converging nozzle, because a lot of converging nozzles operate under conditions where they are not necessarily choked.
RELEVANT VIDEOS
→ Rocketdyne F-1 Mass Flow Rate Example
https://goo.gl/Ezp54H
→ Converging-Diverging Nozzle
https://goo.gl/jrsyoJ
→ Sonic State (Critical, Star)
https://goo.gl/vhjESy
→ Area-Mach Number Relation [CPG]
https://goo.gl/j4FwQX
REFERENCES
► Notes by Matt MacLean
► Modern Compressible Flow, Anderson
► Elements of Gasdynamics, Liepmann and Roshko
► Gas Dynamics, Zucrow and Hoffman
THUMBNAIL IMAGE
By NASA (NASA Human Space Flight Gallery (image link)) [Public domain], via Wikimedia Commons Explained: Nozzle Mass Flow Rate](https://i.ytimg.com/vi/aMTmRCdmvVQ/mqdefault.jpg)
![Explained: Turbojet Thrust Equation
Lets derive the thrust equation for a turbojet engine! In this video Ill show you how to derive the thrust equation for a single-inlet, single-outlet air breathing engine (turbojet is kind of just a buzzword here, because the engine doesnt necessarily need to only be a turbojet).
Yes, this video is heavy on the math, but Im planning on starting a video series called In a Nutshell, which will take some of my math-heavy videos and break them down in to shorter, more easily understandable videos that focus on the big picture. Stay tuned for those.
RELEVANT VIDEOS/LINKS
→ Mass Conservation Derivation
https://goo.gl/Qx7PZ6
→ 1D Mass Conservation
https://goo.gl/hM46LU
→ Momentum Conservation Derivation
https://goo.gl/DuYHcG
→ 1D Momentum Conservation
https://goo.gl/8uo6VM
→ Surface Area Blog Post
https://goo.gl/1s2z2X
→ Turbofan Thrust Equation Derivation
http://www.joshtheengineer.com/2017/04/08/turbofan-thrust-equation/
EXTRA LINKS
► This is the Wikipedia page for Turbojets, and while I dont tend to like Wiki pages for math, take a look at the Net Thrust section.
https://en.wikipedia.org/wiki/Turbojet
ASSUMPTIONS
1) Flow is reversible external to the engine
2) Steady state
3) No viscous forces
4) No heat addition
5) No body forces
6) Velocity only has X-direction component
7) Momentum from fuel flow rate is negligible
THUMBNAIL PICTURE ATTRIBUTION
By Jeff Dahl [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 4.0-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/4.0-3.0-2.5-2.0-1.0)], via Wikimedia Commons
Modified slightly by me Explained: Turbojet Thrust Equation](https://i.ytimg.com/vi/aNyYxVHBSWQ/mqdefault.jpg)