Temperature Measurement

[INRM]

Is it possible to develop a entirely new method of measuring temperature that starts at absolute zero, and isn't really built around the freezing point or boiling point of something, but instead is based purely on average kinetic (heat) levels?

Ideally something linear (20 units would be 10 times 2 units), not exponential like decibels, and based in 10's like most metric systems. Because i'm thinking that would make the ultimate temperature measurement system.

Peter

 

[Ziggurat]

Is it possible to develop a entirely new method of measuring temperature that starts at absolute zero, and isn't really built around the freezing point or boiling point of something, but instead is based purely on average kinetic (heat) levels?

You're too late. It's already been done. It's called kelvin.

BTW, good definitions of temperature aren't based upon energy levels, but upon the relationship between entropy and energy. The distinction is actually important, especially when dealing with things which have different heat capacities.

 

[Solus]

You're too late. It's already been done. It's called kelvin.

BTW, good definitions of temperature aren't based upon energy levels, but upon the relationship between entropy and energy. The distinction is actually important, especially when dealing with things which have different heat capacities.

I was thinking the same thing...

 

[AmateurScientist]

So was everybody else who took high school physics.

AS

 

[Yllanes]

Is it possible to develop a entirely new method of measuring temperature that starts at absolute zero, and isn't really built around the freezing point or boiling point of something, but instead is based purely on average kinetic (heat) levels?

We already have it. The absolute temperature (kelvins, K) . The amplitude of a kelvin is the same as that of 1º C.

There are many definitions of temperature. The most general one, which arises from statistical physics, is

[latex]
\[
T=\left(\frac{\partial U}{\partial S}\right)_V
\]
[/latex]

But basic thermodynamics can give us an operational definition, useful to define practical thermometric scales. We first go to the Law 0 of Thermodynamics, about thermal equilibrium[1]. We give a number to all the states of a system in thermal equilibrium (isotherm). In general, this allows us to define a function of physical parameters that is constant for states in thermal equilibrium. For example, for an ideal gas, all the states with

[latex]
\[
P_1V_1=P_2V_2=P_3V_3=\ldots
\]
[/latex]

define an isotherm. So we can say that a and b are in thermal equilibrium if
P_aV_a = P_b V_b. The next step is to say theta = PV, we label each isotherm with some number. This number is going to be the empirical temperature.

For an ideal gas, the thermometric property is PV, other systems have different thermometric properties

• Column of mercury, alcohol ... in a glass tube -> length.
• Pyrometer -> Stefan-Boltzmann law
• Resistance thermometer.
• Quarz crystal -> vibration frecuency
• Magnetic thermometer -> magnetic susceptibility
• Thermoelectric pair -> emf
• ...

Any of these can provide an empirical definition of temperature. We can say that temperature is the length of the liquid column or the vibration frequency. In general we choose a function, usually linear, [latex]\footnotesize $\theta=ax+b$[/latex] of the thermometric property. To fix the scale we choose two arbitray points and give them values (boiling and freezing point of water, for example). Another alternative is to set b = 0 and choose only a single point. This is what we do nowadays. We measure temperature in kelvins and define a kelvin as 1/273.16 of the temperature of the triple point of water (a state that only happens at a particular pressure where water, vapour and ice are in equilibirum, it's just over 0º C).

Now we have theta = 273.16 x / x_3, where x is some thermometric property and x_3 its value at the triple point. For example, imagine a thermoelectric pair that indicates 2.17 mV at the triple point. If for a certain system we get 6.02 mV, we know the temperature is 273.16*6.02/2.17 = 757.8 K.

The best thermometer we have is the constant volume gas thermometer. The thermometric property is pressure, and the temperature is

[latex]
\[
\theta = T = 273.16 \lim_{p_3\to0}\frac{p}{p_3}
\]
[/latex]

Where T is the ideal gas absolute temperature.

In practice, we cannot use this system all the time, although it is the primary thermometer. The standard scale is called ITS-90 and it is based in many reproducible fixed points, of which only the triple point of water is exact by definition. The thermometer changes for different temperature ranges. Some fixed points are

[latex]
\sffamily\footnotesize
\begin{tabular}{lcc}
\hline
\bfseries Fixed point & $T$ (K) & t ($^\circ$ C)\\
\hline
Helium vapour pressure & 3--5 & -270.15---268.16\\
Hydrogen triple point & 13.80 & -259.35\\
Neon triple point & 24.56 & -248.59\\
Oxygen triple point & 54.36 & -218.79\\
\ldots\\
Water triple point & 273.16 & 0.01\\
\ldots\\
Zinc melting point & 692.67 & 419.53\\
\ldots\\
Gold melting point & 1337.33 & 1064.18\\
\ldots
\end{tabular}
[/latex]

The helium gas thermometer is used until the triple point of neon. Then comes the platinum resistence thermometer, until the melting point of silver and finally radiation thermometers are used.

In short, the theoretical general definition of temperature, and the one a theoretical physicist uses, is

[latex]
\[
T=\left(\frac{\partial U}{\partial S}\right)_V
\]
[/latex]

Which matches your ideas. But a practical definition of a scale that allows for precise measurements over a large range is more involved and requires several stages.
_____
[1] Thermal equilibrium means that the thermodynamical variables of the system remain constant.

 

[INRM]

But Kelvin is based on Celsius, and that's based on the boiling and freezing points of water. What if you had a system that wasn't necessarily calibrated to the boiling or freezing point or something, but simply starting with absolute zero and using energy or radiation levels in a linear system to determine temperature. The boiling points of water would be determined simply by determining the energy level and the fact that the water is boiling

 

[Yllanes]

But Kelvin is based on Celsius, and that's based on the boiling and freezing points of water. What if you had a system that wasn't necessarily calibrated to the boiling or freezing point or something, but simply starting with absolute zero and using energy or radiation levels in a linear system to determine temperature. The boiling points of water would be determined simply by determining the energy level and the fact that the water is boiling

The only way in which kelvins are based on celsius is that a temperature difference of 1 K is equal to a temperature difference of 1 ºC, in other words, a kelvin and a degree celsius have the same size. To make this work, we have to give the triple point of water the arbitrary value 273.16 K. You have to give something an arbitrary value, otehrwise you don't have a scale.

 

[Dr Adequate]

[swiki]Thermodynamic Temperature Scale[/swiki]

 

[Ziggurat]

But Kelvin is based on Celsius, and that's based on the boiling and freezing points of water. What if you had a system that wasn't necessarily calibrated to the boiling or freezing point or something, but simply starting with absolute zero and using energy or radiation levels in a linear system to determine temperature.

The Kelvin scale DOES start at zero and it IS linear (in the sense you mean it). Those are the ONLY two non-arbitrary conditions you can place on a temperature scale. Beyond that, you MUST make an arbitrary choice about the size of each increment, whether it's to set increments based upon energy, radiation, tripple points, or whatever. So ANY other system you could possibly devise which has the first two characteristics will only differ from the Kelvin scale by some constant multiplicative factor. And frankly, there's no point in introducing a new scale like that, because it wouldn't offer any advantage.

Oh, and you can use energy as a temperature scale. Just multiply your temperature by Boltzmann's constant and you get an energy. But of course, energy units are arbitrary too, so that doesn't actually produce a scale any better than Kelvin.

 

[pvt1863]

There is also the Rankine scale, which is Kelvin's imperial counterpart. A change of one degree Rankine is equal to a change in one degree Fahrenheit and zero degrees Rankine is absolute zero. Water freezes at about 492 degrees Rankine.

Part of the problem is that you want temperature to be a measurement of thermal energy, which it is not. Temperature is, in simple terms, a measurement of a mass' ability to give up thermal energy. Temperature is a function of more than just energy -- it is a function of material properties as well. A kg of water has more thermal energy than a kg of Copper at the same temperature because it takes more energy to heat water one degree. In fact, a kg of water can have more thermal energy than a kg of Copper that is hotter than the water. But if you drop that hotter copper into the cooler water, heat will flow from the Copper to the water.

This highlights an important fact about thermodynamics. If no work is done on the system, the net heat transfer will always be from a region of higher temperature to a region of lower temperature. But heat will not always flow from a region of higher thermal energy per unit mass to a region of lower thermal energy per unit mass.

As such, a scale based on thermal energy would be less useful because simply knowing an object's value on this scale would not, by itself, give you enough information about how it would interact with objects around it. A very hot potato, for example, might have less thermal energy per unit mass and rate lower on your desired scale than your hand does, but the potato is still going to burn your hand if you grab it.

Also, what is so special about a scale that sets zero at absolute zero? Such a scale serves no practical purpose in everyday life. Describing the temperature outside in Rankine or Kelvin would be a hassle and wouldn't be anymore useful than using Celsius or Fahrenheit.

 

[Dr Adequate]

Also, what is so special about a scale that sets zero at absolute zero? Such a scale serves no practical purpose in everyday life. Describing the temperature outside in Rankine or Kelvin would be a hassle and wouldn't be anymore useful than using Celsius or Fahrenheit.

It's useful in thermodynamics: see my link above.

 

[pvt1863]

It's useful in thermodynamics: see my link above.

I understand its usefulness in thermodynamics. I am a mechanical/nuclear engineer specializing in thermal hydraulics. I have taken many a thermo or thermo-related course, and I frequently use thermodynamics at work.

I meant in everyday life. Outside of the technical work done by scientists and engineers, there is little usefulness in the broad application of an absolute temperature scale. Saying "it is 295 K outside" or "cook the roast to an internal temperature of 600 degrees R" doesn't help anything.

If the OP was referring to one that would just be used in scientific applications, then the issue itself is pointless. We already have good absolute scales that are used on a regular basis in technical calculations.