Simplifying the First Law of Thermodynamics | Physics by Parth G 

The First Law of Thermodynamics is often said to be a version of the Law of Conservation of Energy... but how is this true?
In this video, we'll be taking a look at how the First Law of Thermodynamics deals with the Internal Energy of a system, as well as understanding the mathematical equation that represents this Law.
Firstly, internal energy is a measure of the state that any system can be found it. Specifically, it is the amount of energy needed to bring the system into the state it's currently in, from an assortment of particles and the like. More info on internal energy can be found here: en.wikipedia.org/wiki/Interna...
The First Law deals with the CHANGE in the internal energy of a system. It tells us that the internal energy will change if there is some form of heating going on, or some form of work being done. Usually the chosen convention is that if the system is heated, then the Q term is positive (and if the system heats the surroundings, then Q is negative). Heat is simply a transfer of energy (to or from the system) WITHOUT any large scale or "macroscopic" forces involved. Work, however, is usually defined the other way. If the system does work on the surroundings, then the W term is positive in the equation. It is negative if the surroundings do work on the system. Work is simply a transfer of energy WITH the involvement of some macroscopic forces (e.g. the gas pushing on a piston). Thus, the full equation becomes Delta U (change in internal energy) = Q (heat transferred to system) - W (work done by system on surroundings).
Sometimes, it is easier to choose the opposite sign convention for work, i.e. W is positive if work is done ON the system, rather than BY the system. In this scenario, the First Law Equation is written Delta U = Q + W. It doesn't really matter which sign convention we choose to use, as long as we are consistent in all our mathematics once the convention has been chosen.
Another important point worth making is that this formulation of the First Law of Thermodynamics only holds if we assume that no matter can be transferred to or from the system (i.e. no particles can enter or leave it). If this were possible, then energy could be transferred this way, and we would need an extra term in the equation to make sure Conservation of Energy was upheld.
Due to the nature of perpetual motion machines (machines that can basically keep moving / extracting energy from nothing forever), it is often said that the First Law is the Law they would have to break in order to exist - they would have to break the idea of conservation of energy.
Thanks so much for watching, new merch down below if you'd like to check it out and support this channel - I really appreciate it!
Many of you have asked about the stuff I use to make my videos, so I'm posting some affiliate links here! I make a small commission if you make a purchase through these links.
A Quantum Physics Book I Enjoy: amzn.to/3sxLlgL
A General Relativity Book I Enjoy: amzn.to/3ytaKwt
My camera (Sony A6400): amzn.to/2SjZzWq
ND Filter: amzn.to/3qoGwHk
Microphone and Stand (Fifine): amzn.to/2OwyWvt
Gorillapod Tripod: amzn.to/3wQ0L2Q
Thanks so much for watching - please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - parth-gs-merch-stand.creator-...
Timestamps:
0:00 - The First Law of Thermodynamics
0:27 - The Law of Conservation of Energy (Energy Cannot Be Created or Destroyed)
0:51 - The Terms in the First Law Equation (and our Gas in a Box System)
1:09 - Internal Energy, U, Contained in the System
2:16 - Heat: Energy Transfer without Macroscopic Forces
3:19 - Work: Energy Transfer with Macroscopic Forces
4:17 - The Overall First Law Equation
4:49 - Clarification About Energy Loss and Gain
5:27 - Sign Conventions and Definition of Q and W
6:18 - Transfer of Matter is NOT Allowed!