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

• Zheng_
In summary: However, in a T-v diagram, v is the independent variable because it is the quantity that is changing with respect to temperature.
Zheng_

## Homework Statement

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

## 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?

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.

Zheng_ said:
My lecture note says that "T-v diagram shows
Zheng_ said:
But T-v means that specific volume(v) is the independent variable right?
I'm not sure what a T-v diagram is. Can you explain?

Zheng_
TomHart said:
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?
Something like this

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.

Zheng_
TomHart said:
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.
Ok. Thanks for the help!

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.

Zheng_
When talking about the gas equation PV=nKT you have three variables and can plot anyone 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)

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

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

CWatters said:
When talking about the gas equation PV=nKT you have three variables and can plot anyone 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)
But if it is a T-v diagram, doesn't it means that v must be the independent variable(x-axis)?

Zheng_ said:
But if it is a T-v diagram, doesn't it means that v must be on the independent variable(x-axis)?
Reference https://www.physicsforums.com/threa...o-b-which-is-the-independent-variable.896384/
Also, the question I'm trying to ask is "if a with respect to b, which is the independent variable?

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

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

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.

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

Normally b would be the independent variable.

## 1. What is the independent variable in a scientific experiment?

The independent variable is the variable that is manipulated or changed by the researcher in an experiment. It is the variable that is believed to have an effect on the dependent variable.

## 2. How is the independent variable determined in a study?

The independent variable is determined by the researcher based on their hypothesis and the purpose of the study. It is usually chosen based on previous research or knowledge about the topic being studied.

## 3. What is the difference between independent and dependent variables?

The independent variable is the variable that is manipulated or changed by the researcher, while the dependent variable is the outcome or result that is measured in response to the changes in the independent variable.

## 4. Can the independent variable change during an experiment?

Yes, in some experiments the independent variable may change or be manipulated multiple times to observe its effects on the dependent variable. However, in other experiments, the independent variable may remain constant.

## 5. How do you determine the relationship between the independent and dependent variables?

The relationship between the independent and dependent variables can be determined by analyzing the data collected from the experiment. This can be done through statistical methods or by visually plotting the data on a graph to observe any patterns or trends.

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