# If a with respect to b, which is the independent variable?

1. Dec 8, 2016

### Zheng_

1. The problem statement, all variables and given/known data

My lecture note says that "T-v diagram shows change in specific volume of a substance with respect to temperature.". Is it correct?
2. Relevant equations

3. The attempt at a solution
If a(Specific Volume) "with respect" to b(Temperature), then b(Temperature) should be the independent variable. But T-v means that specific volume(v) is the independent variable right?

2. Dec 8, 2016

### TomHart

Here are a couple examples I found online:
Dropout voltage also varies with respect to temperature.
The sum of the two voltages remains constant with respect to temperature.
So yes, temperature is the independent variable.

I'm not sure what a T-v diagram is. Can you explain?

3. Dec 8, 2016

### Zheng_

Something like this

4. Dec 8, 2016

### TomHart

Okay. Then if what he said is in reference to a chart like the one above, then it appears that he should have said, "temperature with respect to volume". You may want to ask him for clarification.

5. Dec 8, 2016

### Zheng_

Ok. Thanks for the help!

6. Dec 8, 2016

### TomHart

One of the phrases that always bothered me was describing a chart using the term "vs". As an example, saying "voltage vs. current" describes a graph where voltage is the independent variable (x axis) and current is the dependent variable (y axis). It always seemed to me that chart should have been called "current vs. voltage" - that saying "vs." should be equivalent to saying "with respect to". But that's not how it's done.

So in your T-v chart example, one should say "volume vs. temperature. But to me that seems backward.

7. Dec 8, 2016

### CWatters

When talking about the gas equation PV=nKT you have three variables and can plot any one against any other. Any of the three can be the independent variable so there are 6 possible graphs. I think it's only by convention that we normally stick to these three...

T-V Diagrams (Y axis = Temperature, X axis = Volume)
P-V Diagrams (Y axis = Pressure, X axis = Volume
Phase Diagrams (Y axis = Pressure, X axis = Temperature)

8. Dec 8, 2016

### CWatters

Regarding Ohms law... Most people know it as V=IR so you might expect the Y axis to be Voltage, but if you look up the definition you find..

https://en.wikipedia.org/wiki/Ohm's_law

9. Dec 8, 2016

### Zheng_

But if it is a T-v diagram, doesn't it means that v must be the independent variable(x-axis)?

10. Dec 8, 2016

### Zheng_

Also, the question I'm trying to ask is "if a with respect to b, which is the independent variable?

R
Also, if a with respect to b, which one is the independent variable?

Reference https://www.physicsforums.com/threa...o-b-which-is-the-independent-variable.896384/

11. Dec 9, 2016

### CWatters

T-V diagrams are usually drawn with T on the y axis and V on the x axis, however if someone was to do an experiment where T was the independent variable they would probably still plot T on the y-axis because people are more familiar with seeing T-V diagrams that way around. It makes it easier to compare data with other experiments.

Normally b would be the independent variable.