# How Is Temperature Defined in Kelvin Using Fundamental Units?

• "pi"mp
In summary, the conversation discusses defining temperature in Kelvin using fundamental units of mass, length, and time. One suggestion is to use kT=hf, where f is the frequency of oscillation of Cs-133 radiation at that temperature. Another suggestion is to use Planck units, with fixed values for k and h, and an arbitrary value for f. Both methods aim to make units less dependent on specific setups.
"pi"mp
Hi all,
I'm reading through Zwiebach's String Theory text on my own and am thinking about one of his very elementary exercises on "units." We are asked to define temperature in Kelvin with reference to the fundamental units of mass, length, and time. My thought is the following:

We take kT=hf where here f is the frequency of oscillation of Cs-133 radiation at that temperature since that is how the "second" is defined. Then we will have defined the temperature T (in Kelvin) in terms of only numerical quantities whose value we know (k and h) and f.

I'm not very confident about this at all but I'm not sure how else to do it.

That is the usual way to make units less dependent on specific setups, indeed. I think "fundamental units of mass, length and time" are the Planck units here, not specific transition in some specific isotope.

Ah okay, so how would I go about constructing the Kelvin that way?

You can just use kT=hf as definition, with fixed values for k and h (in Planck units, h has a known value anyway). The value of k is arbitrary.

hmm okay. But then what would "f" be? I thought you said we ought not refer to a specific isotope or anything like that.

The Planck units have something you can use there.

## 1. What is the definition of Kelvin?

The Kelvin is the base unit of temperature in the International System of Units (SI). It is defined as 1/273.16 of the thermodynamic temperature of the triple point of water, which is the point at which water exists in its liquid, solid, and gaseous states simultaneously.

## 2. How does the definition of Kelvin differ from other temperature scales?

The definition of Kelvin is unique because it is based on the fundamental principles of thermodynamics, rather than a physical object or substance. This makes it a universal and constant unit of temperature, whereas other scales may change based on the properties of the substance they are measuring.

## 3. What is the significance of the triple point of water in the definition of Kelvin?

The triple point of water is a crucial reference point in the definition of Kelvin because it is a fixed and reproducible state of water that can be used to accurately measure temperature. It also provides a natural and stable reference point for the Kelvin scale.

## 4. Is the definition of Kelvin subject to change?

The definition of Kelvin is not subject to change as it is based on fundamental physical principles and is defined by the International Bureau of Weights and Measures (BIPM). However, the scale used to measure temperature in Kelvins may be adjusted to improve accuracy and precision.

## 5. How is the definition of Kelvin used in scientific research?

The definition of Kelvin is used in scientific research to accurately measure and compare temperatures across different systems and experiments. It is also used to study the behavior of matter and energy at extreme temperatures, such as in astrophysics and thermodynamics.

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