Measurement of heat as an interval measurement or a ratio measurement

[jonohashmo543]

TL;DR Summary

determining if a measurement of heat is absolute or arbitrary.

Hello!

I am new to this forum and I'm not even sure if this is the right place to ask but here goes:

I am studying Research Methods. I got to the part where the teacher is teaching us about levels of measurement. They said that there are a few levels but the two that are significant to my question are Interval and Ratio.

Interval: As my teacher explained, shoe size measurement is an example of an interval measurement. If someone has a shoe size of 0, we do not think that their feet have 0 length. Similarly, if someone has a shoe size of 4, we do not think that someone with a shoe size of 8 has feet that are literally two times the length of the person with size 4 shoes.

Ratio: A ratio measurement is like the metric system. We know that 0 literally means 0, and that 8cm is literally twice as long as 4cm.

Then the teacher gave Temperature as an example for Interval measurement. That confused me greatly. If we look at Fahrenheit for example, does 0 F have any significance? Is it absolute? Similarly, can we say that 60 F is literally "twice as hot" as 30 F? What if the same questions were asked in Celsius? Or Kelvin?

Basically, I'm wondering if there is an agreed upon absolute measurement for heat, (like metric system in shoe size example) and scales like Fahrenheit Celsius and Kelvin are just plopped on top of that absolute measurement with increments of their own?

Sorry if this is irrelevant to this forum, I just don't really know where to ask this question.

Thanks!
Jonathan

 

[gmax137]

There are temperature scales where zero is "really zero." These are called "absolute temperature scales." The Rankine and Kelvin scales are "absolute."

I'm sure the wiki page on the Fahrenheit scale explains the significance of zero degrees F.

Similarly, can we say that 60 F is literally "twice as hot" as 30 F? What if the same questions were asked in Celsius? Or Kelvin?

If you convert these values (60 and 30F) to Celsius (or Kelvin) you will see that "twice as hot" is not right. But if you convert to two different absolute scales (say, R and K) then the ratio should be the same. That's the beauty of absolute scales.

 

[jbriggs444]

Basically, I'm wondering if there is an agreed upon absolute measurement for heat, (like metric system in shoe size example) and scales like Fahrenheit Celsius and Kelvin are just plopped on top of that absolute measurement with increments of their own?

When I went to school (lo those many years ago) we were taught that "heat" is a transfer of thermal energy. In the same way that "impulse" is a transfer of momentum and "work" is a transfer of mechanical energy.

For this notion of heat there are definitely absolute units. Such as the BTU, the Calorie or the Joule. The zero on the each scale indicates that no thermal energy is transferred.

However, you may be thinking of "heat" as a measure of how much thermal energy is present in a body. For typical everyday conditions, the amount of thermal energy in a body goes to zero as temperature goes toward absolute zero. For an ideal gas, this is exactly true. For real substances it is only approximately true.

For every day conditions, "temperature" closely matches kinetic energy per particle per degree of freedom. See this link. Following this pattern, we would expect zero energy at zero Kelvin. But when things get cold, it is useful to shift to a different and more general definition of temperature in terms of the ratio of the incremental change in entropy divided by the incremental change in thermal energy:$$\frac{1}{T}=\frac{dS}{dE}$$[There are some caveats].

This definition eliminates the requirement that energy be zero at absolute zero. It also makes the actual value of thermal energy irrelevant. All that matters is how it changes relative to entropy. This definition also makes absolute zero unachievable and negative temperatures achievable. However, because the definition is for inverse temperature, the scale is a bit strange. All negative temperatures are "hotter" than all positive temperatures.

Here is a link to a Wiki article about thermodynamic temperature that may help you sleep tonight.

 

[jonohashmo543]

There are temperature scales where zero is "really zero." These are called "absolute temperature scales." The Rankine and Kelvin scales are "absolute."

I'm sure the wiki page on the Fahrenheit scale explains the significance of zero degrees F.If you convert these values (60 and 30F) to Celsius (or Kelvin) you will see that "twice as hot" is not right. But if you convert to two different absolute scales (say, R and K) then the ratio should be the same. That's the beauty of absolute scales.

Thank you so much for your reply!

When converting 60 and 30 F to R or K the values are still not twice as much... so the absolute scales also shift in different ways?

 

[jonohashmo543]

When I went to school (lo those many years ago) we were taught that "heat" is a transfer of thermal energy. In the same way that "impulse" is a transfer of momentum and "work" is a transfer of mechanical energy.

For this notion of heat there are definitely absolute units. Such as the BTU, the Calorie or the Joule. The zero on the each scale indicates that no thermal energy is transferred.

However, you may be thinking of "heat" as a measure of how much thermal energy is present in a body. For typical everyday conditions, the amount of thermal energy in a body goes to zero as temperature goes toward absolute zero. For an ideal gas, this is exactly true. For real substances it is only approximately true.

For every day conditions, "temperature" closely matches kinetic energy per particle per degree of freedom. See this link. Following this pattern, we would expect zero energy at zero Kelvin. But when things get cold, it is useful to shift to a different and more general definition of temperature in terms of the ratio of the incremental change in entropy divided by the incremental change in thermal energy:$$\frac{1}{T}=\frac{dS}{dE}$$[There are some caveats].

This definition eliminates the requirement that energy be zero at absolute zero. It also makes the actual value of thermal energy irrelevant. All that matters is how it changes relative to entropy. This definition also makes absolute zero unachievable and negative temperatures achievable. However, because the definition is for inverse temperature, the scale is a bit strange. All negative temperatures are "hotter" than all positive temperatures.

Here is a link to a Wiki article about thermodynamic temperature that may help you sleep tonight.

Thank you so much for your beautifully detailed reply!

Unfortunately, as someone who did not study physics at a high level, this is beyond my understanding. But from what I do understand, it seems like all scales of "temperature" are not ratio scales, since absolute zero is impossible to achieve in "temperature" (even though it sounds like that in "heat" it is possible).

Is that true?

Thanks:)

 

[jbriggs444]

But from what I do understand, it seems like all scales of "temperature" are not ratio scales, since absolute zero is impossible to achieve in "temperature"

In my view, absolute temperature (e.g. Kelvin or Rankine) is a ratio scale. We can see this in various formulae from thermodynamics and chemistry.

For instance, the ideal gas law ($pV=nRT$), Charle's law ($V=kT$) or Carnot efficiency ($n_\text{max} = \frac{T_L}{T_H}$)

Double the temperature and you double the pressure. That sounds like a ratio situation to me.

Do not get too hung up on terminology. If you understand how things work, the names under which you classify them are of minor importance. Now if we could only convince your teachers of that...

 

[gmax137]

When converting 60 and 30 F to R or K the values are still not twice as much... so the absolute scales also shift in different ways?

Here's 60 and 30F in other scales. The bottom row is the ratio of "60" to "30." For F and C scales, it is just nonsense, because the scales are not absolute. Looking at the R and K scales, even though the particular values differ, the ratio is the same. A temperature of 60F is in a sense, "1.06 times as hot" as 30F.

$$
\begin {array}{|c|c|c|c|}
\hline F&C&R&K \\
\hline 60&15.56&520&289 \\
\hline 30&-1.11&490&272 \\
\hline 2.00&-14.02&1.06&1.06 \\
\hline
\end {array}
$$

 

[jonohashmo543]

In my view, absolute temperature (e.g. Kelvin or Rankine) is a ratio scale. We can see this in various formulae from thermodynamics and chemistry.

For instance, the ideal gas law ($pV=nRT$), Charle's law ($V=kT$) or Carnot efficiency ($n_\text{max} = \frac{T_L}{T_H}$)

Double the temperature and you double the pressure. That sounds like a ratio situation to me.

Do not get too hung up on terminology. If you understand how things work, the names under which you classify them are of minor importance. Now if we could only convince your teachers of that...

Hahahahaha! If only indeed. Thanks so much for your help in this:)

 

[jonohashmo543]

Here's 60 and 30F in other scales. The bottom row is the ratio of "60" to "30." For F and C scales, it is just nonsense, because the scales are not absolute. Looking at the R and K scales, even though the particular values differ, the ratio is the same. A temperature of 60F is in a sense, "1.06 times as hot" as 30F.

$$
\begin {array}{|c|c|c|c|}
\hline F&C&R&K \\
\hline 60&15.56&520&289 \\
\hline 30&-1.11&490&272 \\
\hline 2.00&-14.02&1.06&1.06 \\
\hline
\end {array}
$$

This is so interesting!!! Thanks so much for this! I completely understand now:)

 

[sophiecentaur]

TL;DR Summary: determining if a measurement of heat is absolute or arbitrary.

Sorry if this is irrelevant to this forum,

No. It's highly relevant to bear this in mind whenever trying to community a value to someone. The only quantities that are rock solid are integers. "Seven footballs" is hard to mis-interpret but, even integer values may not be bomb proof. "Three potatoes" in a recipe book won't tell you how much actual potato mass is needed.

TL;DR Summary: determining if a measurement of heat is absolute or arbitrary.

Interval: As my teacher explained, shoe size measurement is an example of an interval measurement.

This is all about quantisation; if there is a continuum of possible lengths and only so many 'bins' to put them in, we have to use quantisation. This applies whenever data is 'digitised'.

If we want a meaningful relationship between the bins which we choose and scientific equations which assume a continuous range of possible values then the bin values (intervals) need to be chosen more carefully than is done in the case of shoes. For shoes, the bins are chosen to fit the requirements of the market and the convenience of the manufacturing and supply chain. If the quantisation (step sizes) is arbitrary then we can't apply simple algebraic formulae (e.g. SUVAT equations). The quantisation of shoe sizes is non-linear.

TL;DR Summary: determining if a measurement of heat is absolute or arbitrary.

Then the teacher gave Temperature as an example for Interval measurement.

A minefield, here. Commonly stated temperatures are quantised and with an Origin (the zero point) that is arbitrary. But we certainly need to use intervals less than 1C (even on our central heating control)

People try to talk in terms of "twice as warm as it was yesterday" which is total nonsense and very misleading. The Centigrade scale has one serious advantage in which we can recognise Zero C and 100C by what we can actually see happens to water.