No σ on σ

Although its measurement was considered an experimental nightmare for decades, the Stefan–Boltzmann constant was assigned an exact value in 2019. Massimiliano Malgieri and Pasquale Onorato explain what this story teaches us.

Because of their relationship to planetary radiative equilibrium and the greenhouse effect, the Stefan–Boltzmann law and constant are important factors in physics education. Students hold a variety of misconceptions regarding radiative exchange processes, which hinder their conceptual understanding of what determines planetary temperature. By measuring the electric power absorbed by a tungsten filament as a function of its temperature, they can derive the functional form of the Stefan–Boltzmann law as part of their lab classes. This also teaches them a lesson about the way science proceeds.

This is a preview of subscription content, access via your institution

Access options

/* style specs start */
style{display:none!important}.LiveAreaSection-193358632 *{align-content:stretch;align-items:stretch;align-self:auto;animation-delay:0s;animation-direction:normal;animation-duration:0s;animation-fill-mode:none;animation-iteration-count:1;animation-name:none;animation-play-state:running;animation-timing-function:ease;azimuth:center;backface-visibility:visible;background-attachment:scroll;background-blend-mode:normal;background-clip:borderBox;background-color:transparent;background-image:none;background-origin:paddingBox;background-position:0 0;background-repeat:repeat;background-size:auto auto;block-size:auto;border-block-end-color:currentcolor;border-block-end-style:none;border-block-end-width:medium;border-block-start-color:currentcolor;border-block-start-style:none;border-block-start-width:medium;border-bottom-color:currentcolor;border-bottom-left-radius:0;border-bottom-right-radius:0;border-bottom-style:none;border-bottom-width:medium;border-collapse:separate;border-image-outset:0s;border-image-repeat:stretch;border-image-slice:100%;border-image-source:none;border-image-width:1;border-inline-end-color:currentcolor;border-inline-end-style:none;border-inline-end-width:medium;border-inline-start-color:currentcolor;border-inline-start-style:none;border-inline-start-width:medium;border-left-color:currentcolor;border-left-style:none;border-left-width:medium;border-right-color:currentcolor;border-right-style:none;border-right-width:medium;border-spacing:0;border-top-color:currentcolor;border-top-left-radius:0;border-top-right-radius:0;border-top-style:none;border-top-width:medium;bottom:auto;box-decoration-break:slice;box-shadow:none;box-sizing:border-box;break-after:auto;break-before:auto;break-inside:auto;caption-side:top;caret-color:auto;clear:none;clip:auto;clip-path:none;color:initial;column-count:auto;column-fill:balance;column-gap:normal;column-rule-color:currentcolor;column-rule-style:none;column-rule-width:medium;column-span:none;column-width:auto;content:normal;counter-increment:none;counter-reset:none;cursor:auto;display:inline;empty-cells:show;filter:none;flex-basis:auto;flex-direction:row;flex-grow:0;flex-shrink:1;flex-wrap:nowrap;float:none;font-family:initial;font-feature-settings:normal;font-kerning:auto;font-language-override:normal;font-size:medium;font-size-adjust:none;font-stretch:normal;font-style:normal;font-synthesis:weight style;font-variant:normal;font-variant-alternates:normal;font-variant-caps:normal;font-variant-east-asian:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-position:normal;font-weight:400;grid-auto-columns:auto;grid-auto-flow:row;grid-auto-rows:auto;grid-column-end:auto;grid-column-gap:0;grid-column-start:auto;grid-row-end:auto;grid-row-gap:0;grid-row-start:auto;grid-template-areas:none;grid-template-columns:none;grid-template-rows:none;height:auto;hyphens:manual;image-orientation:0deg;image-rendering:auto;image-resolution:1dppx;ime-mode:auto;inline-size:auto;isolation:auto;justify-content:flexStart;left:auto;letter-spacing:normal;line-break:auto;line-height:normal;list-style-image:none;list-style-position:outside;list-style-type:disc;margin-block-end:0;margin-block-start:0;margin-bottom:0;margin-inline-end:0;margin-inline-start:0;margin-left:0;margin-right:0;margin-top:0;mask-clip:borderBox;mask-composite:add;mask-image:none;mask-mode:matchSource;mask-origin:borderBox;mask-position:0 0;mask-repeat:repeat;mask-size:auto;mask-type:luminance;max-height:none;max-width:none;min-block-size:0;min-height:0;min-inline-size:0;min-width:0;mix-blend-mode:normal;object-fit:fill;object-position:50% 50%;offset-block-end:auto;offset-block-start:auto;offset-inline-end:auto;offset-inline-start:auto;opacity:1;order:0;orphans:2;outline-color:initial;outline-offset:0;outline-style:none;outline-width:medium;overflow:visible;overflow-wrap:normal;overflow-x:visible;overflow-y:visible;padding-block-end:0;padding-block-start:0;padding-bottom:0;padding-inline-end:0;padding-inline-start:0;padding-left:0;padding-right:0;padding-top:0;page-break-after:auto;page-break-before:auto;page-break-inside:auto;perspective:none;perspective-origin:50% 50%;pointer-events:auto;position:static;quotes:initial;resize:none;right:auto;ruby-align:spaceAround;ruby-merge:separate;ruby-position:over;scroll-behavior:auto;scroll-snap-coordinate:none;scroll-snap-destination:0 0;scroll-snap-points-x:none;scroll-snap-points-y:none;scroll-snap-type:none;shape-image-threshold:0;shape-margin:0;shape-outside:none;tab-size:8;table-layout:auto;text-align:initial;text-align-last:auto;text-combine-upright:none;text-decoration-color:currentcolor;text-decoration-line:none;text-decoration-style:solid;text-emphasis-color:currentcolor;text-emphasis-position:over right;text-emphasis-style:none;text-indent:0;text-justify:auto;text-orientation:mixed;text-overflow:clip;text-rendering:auto;text-shadow:none;text-transform:none;text-underline-position:auto;top:auto;touch-action:auto;transform:none;transform-box:borderBox;transform-origin:50% 50%0;transform-style:flat;transition-delay:0s;transition-duration:0s;transition-property:all;transition-timing-function:ease;vertical-align:baseline;visibility:visible;white-space:normal;widows:2;width:auto;will-change:auto;word-break:normal;word-spacing:normal;word-wrap:normal;writing-mode:horizontalTb;z-index:auto;-webkit-appearance:none;-moz-appearance:none;-ms-appearance:none;appearance:none;margin:0}.LiveAreaSection-193358632{width:100%}.LiveAreaSection-193358632 .login-option-buybox{display:block;width:100%;font-size:17px;line-height:30px;color:#222;padding-top:30px;font-family:Harding,Palatino,serif}.LiveAreaSection-193358632 .additional-access-options{display:block;font-weight:700;font-size:17px;line-height:30px;color:#222;font-family:Harding,Palatino,serif}.LiveAreaSection-193358632 .additional-login>li:not(:first-child)::before{transform:translateY(-50%);content:””;height:1rem;position:absolute;top:50%;left:0;border-left:2px solid #999}.LiveAreaSection-193358632 .additional-login>li:not(:first-child){padding-left:10px}.LiveAreaSection-193358632 .additional-login>li{display:inline-block;position:relative;vertical-align:middle;padding-right:10px}.BuyBoxSection-683559780{display:flex;flex-wrap:wrap;flex:1;flex-direction:row-reverse;margin:-30px -15px 0}.BuyBoxSection-683559780 .box-inner{width:100%;height:100%}.BuyBoxSection-683559780 .readcube-buybox{background-color:#f3f3f3;flex-shrink:1;flex-grow:1;flex-basis:255px;background-clip:content-box;padding:0 15px;margin-top:30px}.BuyBoxSection-683559780 .subscribe-buybox{background-color:#f3f3f3;flex-shrink:1;flex-grow:4;flex-basis:300px;background-clip:content-box;padding:0 15px;margin-top:30px}.BuyBoxSection-683559780 .subscribe-buybox-nature-plus{background-color:#f3f3f3;flex-shrink:1;flex-grow:4;flex-basis:100%;background-clip:content-box;padding:0 15px;margin-top:30px}.BuyBoxSection-683559780 .title-readcube,.BuyBoxSection-683559780 .title-buybox{display:block;margin:0;margin-right:10%;margin-left:10%;font-size:24px;line-height:32px;color:#222;padding-top:30px;text-align:center;font-family:Harding,Palatino,serif}.BuyBoxSection-683559780 .title-asia-buybox{display:block;margin:0;margin-right:5%;margin-left:5%;font-size:24px;line-height:32px;color:#222;padding-top:30px;text-align:center;font-family:Harding,Palatino,serif}.BuyBoxSection-683559780 .asia-link{color:#069;cursor:pointer;text-decoration:none;font-size:1.05em;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:1.05em6}.BuyBoxSection-683559780 .access-readcube{display:block;margin:0;margin-right:10%;margin-left:10%;font-size:14px;color:#222;padding-top:10px;text-align:center;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:20px}.BuyBoxSection-683559780 .access-asia-buybox{display:block;margin:0;margin-right:5%;margin-left:5%;font-size:14px;color:#222;padding-top:10px;text-align:center;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:20px}.BuyBoxSection-683559780 .access-buybox{display:block;margin:0;margin-right:10%;margin-left:10%;font-size:14px;color:#222;opacity:.8px;padding-top:10px;text-align:center;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:20px}.BuyBoxSection-683559780 .price-buybox{display:block;font-size:30px;color:#222;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;padding-top:30px;text-align:center}.BuyBoxSection-683559780 .price-buybox-to{display:block;font-size:30px;color:#222;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;text-align:center}.BuyBoxSection-683559780 .price-info-text{font-size:16px;padding-right:10px;color:#222;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif}.BuyBoxSection-683559780 .price-value{font-size:30px;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif}.BuyBoxSection-683559780 .price-per-period{font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif}.BuyBoxSection-683559780 .price-from{font-size:14px;padding-right:10px;color:#222;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:20px}.BuyBoxSection-683559780 .issue-buybox{display:block;font-size:13px;text-align:center;color:#222;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:19px}.BuyBoxSection-683559780 .no-price-buybox{display:block;font-size:13px;line-height:18px;text-align:center;padding-right:10%;padding-left:10%;padding-bottom:20px;padding-top:30px;color:#222;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif}.BuyBoxSection-683559780 .vat-buybox{display:block;margin-top:5px;margin-right:20%;margin-left:20%;font-size:11px;color:#222;padding-top:10px;padding-bottom:15px;text-align:center;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:17px}.BuyBoxSection-683559780 .tax-buybox{display:block;width:100%;color:#222;padding:20px 16px;text-align:center;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;line-height:NaNpx}.BuyBoxSection-683559780 .button-container{display:flex;padding-right:20px;padding-left:20px;justify-content:center}.BuyBoxSection-683559780 .button-container>*{flex:1px}.BuyBoxSection-683559780 .button-container>a:hover,.Button-505204839:hover,.Button-1078489254:hover,.Button-2496381730:hover{text-decoration:none}.BuyBoxSection-683559780 .readcube-button{background:#fff;margin-top:30px}.BuyBoxSection-683559780 .button-asia{background:#069;border:1px solid #069;border-radius:0;cursor:pointer;display:block;padding:9px;outline:0;text-align:center;text-decoration:none;min-width:80px;margin-top:75px}.BuyBoxSection-683559780 .button-label-asia,.ButtonLabel-3869432492,.ButtonLabel-3296148077,.ButtonLabel-1651148777{display:block;color:#fff;font-size:17px;line-height:20px;font-family:-apple-system,BlinkMacSystemFont,”Segoe UI”,Roboto,Oxygen-Sans,Ubuntu,Cantarell,”Helvetica Neue”,sans-serif;text-align:center;text-decoration:none;cursor:pointer}.Button-505204839,.Button-1078489254,.Button-2496381730{background:#069;border:1px solid #069;border-radius:0;cursor:pointer;display:block;padding:9px;outline:0;text-align:center;text-decoration:none;min-width:80px;max-width:320px;margin-top:10px}.Button-505204839 .readcube-label,.Button-1078489254 .readcube-label,.Button-2496381730 .readcube-label{color:#069}
/* style specs end */

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

References

Cohen, E. R. & Taylor, B. N. Rev. Mod. Phys. 59, 1121–1148 (1987).

Article
ADS

Google Scholar
Quinn, T. J. & Martin, J. E. Philos. Trans. R. Soc. A 316, 85–189 (1985).

ADS

Google Scholar

Download references

Author information

Authors and Affiliations

Department of Physics, University of Pavia, Pavia, Italy

Massimiliano Malgieri
Department of Physics, University of Trento, Trento, Italy

Pasquale Onorato

Authors

Massimiliano Malgieri

View author publications

You can also search for this author in
PubMed Google Scholar
Pasquale Onorato

View author publications

You can also search for this author in
PubMed Google Scholar

Corresponding authors

Correspondence to
Massimiliano Malgieri or Pasquale Onorato.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Malgieri, M., Onorato, P. No σ on σ.
Nat. Phys. 19, 1734 (2023). https://doi.org/10.1038/s41567-023-02273-3

Download citation

Published: 09 November 2023
Issue Date: November 2023
DOI: https://doi.org/10.1038/s41567-023-02273-3