# Do Voltage/Temperature measure Energy; Fields/Pressure measure Force?

1. Aug 17, 2013

### 541099

Would it be correct to call Voltage and Temperature intensive measures of Energy, and call Electric Field and Pressure intensive measures of the potential for Force generation?

If so, is Voltage (Potential Energy) used to generate a force on a charged particle (by way of an Electrical Field), while Temperature (Kinetic Energy) is used to generate a force on a particle with mass (by way of Pressure)?

If this is also true, then what are their conjugate variables?
Am I pairing these up properly...?
Pressure...Volume
Temperature...Entropy
Voltage...Total Charge? Total Charge Flow?
Electric Field...Charge Displacement (Dipole moment?)

I'm a pre-medical student studying for the MCAT. I was reinforcing my foundations in physics and got a bit carried away. Sorry if some of the technical language isn't correct. In any case, I'm curious now.

2. Aug 19, 2013

### Khashishi

It sounds like you are too focused on the terminology rather than the concept behind it. Physicists make up terms all the time, and say stuff like pressure and temperature are "generalized forces". Really, it's just an analogy, and pressure and temperature aren't the same thing as force. I suppose it can be hard to pick out when a term is actually important, and when it's not. The intensive variables act like "generalized forces" but they aren't forces. The extensive variables act like "generalized displacements". Neither one is an energy. Rather, you get energy by combining the generalized force and generalized displacement.

For example, including your first three pairs of conjugate variables:
$dU = P dV + T dS + \phi dQ$
where P is pressure, V is volume, T is temperature, S is entropy, phi is voltage, Q is charge
P, T, and V are intrinsic variables or "generalized forces"
S, phi, and Q are extrinsic variables or "generalized displacements"
It's not important to remember the terms "generalized force" or "generalized displacement". They are just made up.
It's an analogy to the fact that (change in energy) is force times displacement.

Of course, you can add as many conjugate variable pairs into your energy equation as you want. It depends on your system you are working with.

I wasn't sure about your fourth conjugate pair, but after thinking about it, it seems ok. But it might be clearer if stated as:
electric field...polarization

another one is
magnetic field...magnetization

3. Aug 19, 2013

### 541099

Khashishi, I couldn't figure out how to articulate it until now, but this was my reasoning.

I was playing around with some of the circuit equations and saw that PE=V/q, where PE is potential energy, V is voltage, and q is charge. This gave me the impression that Voltage could also be thought of as how much Energy can be used to move a single charged particle across a distance.

In this same way I saw that E=F/q, where E is Electric Field, F is Electric Force, and q is charge. I thought this might imply that Electric Field could also be thought of as a measure of how much Force could be generated to move a charged particle over time.

Is this way of thinking inaccurate?

4. Aug 20, 2013

### Andrew Mason

As Khashishi says, don't get hung up on the concept of "generalized forces" and "generalized displacements". These are not helpful terms, particularly when you are starting to learn physics.

Energy has units of force x displacement. That is because energy is defined as the ability to do work and work is defined as a displacement multiplied by the component of force in the direction of the displacement. Someone thought it helpful to come up with the concept of generalized forces (most of which are not forces), and generalized displacements, (most of which are not displacements), which when multiplied together result in energy.

Voltage x charge = energy but that does not suggest that charge is analogous to a displacement. It is not. Voltage is not a generalized force either. But that is confusing because voltage is often referred to as "electromotive force" (because it can be thought of as pushing charges through a circuit). Voltage is energy per unit charge or force per unit charge x a distance. The field, E, is force per unit charge. E x charge does not equal energy. E x charge x displacement = energy.

Temperature is not even analogous to a force and entropy is not analogous to a displacement. But multiplied together, TS, has units of energy (reversible heat flow). I have no idea why anyone would use the concepts of generalized force and displacement to describe these variables unless they were intending to confuse students.

AM

5. Aug 20, 2013

### 541099

These concepts are still just not sitting comfortably, yet.
Are there any books someone could recommend reading that would elucidate this better? I don't care if they're textbooks or any other kind.