# General equation for Energy problems? (system/internal/thermal/kinetic)

So, I'm working on my physics homework and so far, in reading all the explanations, have come across so many different equations (all for energy). I've tried to tie it all into one equation because I just never know which one to use or what to include, etc (and have looked in FOUR textbooks already).

So, these are the equations I've come across in different explanations: **deltaE=W ( and then from this they turned it into deltaKtrans+ deltaEinternal= FdeltaX ) **Ethermal= Q + other **deltaEsystem= W+ Q + other energy transfer **deltaE=W **Work (non conservative) = delta E= delta Kinetic energy + delta Potential energy

So, whenever It's an energy problem, my first instinct is to use the "Work(nonconservative)= delta Kinetic + delta Potential" but sometimes that won't be sufficient...when they introduce things like Einternal and Ktranslational.

Would something like "delta E system = transferred energy" work for all problems? Where Delta E system = kinetic, potential, and internal energy? and energy transferred = Q + W?

Also, what even is the difference between E system, E internal, and E thermal. And is Ktranslational part of the system's kinetic energy or the internal energy or??

Can you see I'm really confused? I've tried reading from four different textbooks already and gone to office hours but no one has any concrete answer as to HOW I'm supposed to know which energies are involved in a problem & which equation I'm supposed to use / which variables of an equation to ignore??

Sorry for the long question, but can someone PLEASE help me.

• -1. Unclear. It is difficult to understand your difficulties based on such a general description. It is much easier to understand and discuss them within the context of a specific problem. ... Also, please learn and useMathJax for your equations. – sammy gerbil Mar 26 '17 at 1:40
• Please use MathJax or Latex, it is very cumbersome to read the current formatting. – electronpusher Mar 28 '17 at 0:25

## 1 Answer

I have trouble reading the format of your text, but here're my thoughts. Use this:$$Q+W=\Delta E$$ Where $\Delta E$ is the total energy of the system. Total energy is the sum of kinetic, potential, thermal (and chemical, and nuclear, and radiant and so on ... usually ignored in intro physics class).

In order to use this correctly you have to carefully define which objects are inside your system and which objects are outside. Draw a dotted line around the objects in your system. Any force that cross the boundary of the system (the dotted line) is an external force and does work which we account for in $W$. Forces that are entirely inside the system do no external work so they don't contribute to $W$, but they do transfer energy among the components of the total energy: kinetic to potential, kinetic to thermal, chemical to kinetic, etc. $Q$ is heat that crosses the boundary, not heat that is transferred from one object in the system to another.

This business is handled poorly in just about every textbook I've seen. One approach that I think is particularly misleading is to single out non-conservative forces. The intention is to account for conservative forces by the introduction of potential energy. But non-conservative internal forces are not intended to be included in $W_{NC}$. And an external conservative force does not contribute to the potential energy of the system, and should be dealt with as a contribution to work.

• Physicists tend to avoid situations with non-conservative forces, because if you model the system in enough detail (e.g. at the level of interactions between elementary particles) all the forces are conservative. Non-conservative forces can be considered as just "approximations" useful for modelling the large-scale behaviour of systems (e.g. friction, viscosity, etc) but (as in a quote by Feynman) physicists usually leave dealing with "real world stuff" like that to engineers, rather than doing it themselves! – alephzero Mar 26 '17 at 3:51
• @alephzero At the microscopic and fundamental level, you are right. But that doesn't help the student in Physics 101 where friction is presented without any comment on fundamental origins. Friction is a perfectly valid phenomenon that simplifies poorly understood and very complicated physics, and can be modeled simply. I agree that the micro physics should be discussed hand-in-hand with the phenomenology, but that isn't happening. – garyp Mar 26 '17 at 12:27