Earth temperature from the Stefan-Boltzmann Law

stefan-boltzmann-revisited.ipynb

The result for P0 = E/H = 14e13 watts is incorrect in the post:
https://wildpeaches.xyz/blog/stefan-boltzmann-revisited/

The correct value, as in this gist, is 2.0421118721461188e13 (~20.42 TW)

This is in line with https://en.wikipedia.org/wiki/World_energy_supply_and_consumption (19.6TW 2021).

14e13 watts is around 7 times higher, which made me jump a bit

Lars, Thanks for letting me know! I'll look into it and figure out what I did wrong. Hopefully it's just a typo in the text since a factor of ~7 is kind of strange. John

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On Mon, Mar 3, 2025 at 2:39 AM Lars Ekman ***@***.***> wrote: ***@***.**** commented on this gist. ------------------------------ The result for P0 = E/H = 14e13 watts is incorrect in the post: https://wildpeaches.xyz/blog/stefan-boltzmann-revisited/ The correct value, as in this gist, is 2.0421118721461188e13 (~20.42 TW) This is in line with https://en.wikipedia.org/wiki/World_energy_supply_and_consumption (19.6TW 2021). 14e13 watts is around 7 times higher, which made me jump a bit — Reply to this email directly, view it on GitHub <https://gist.github.com/XerxesZorgon/6b056a34ee85fb4322053b8265f3b301#gistcomment-5466096> or unsubscribe <https://github.com/notifications/unsubscribe-auth/AC3KQPIS25JHT4OYQ2WDRAL2SQBLBBFKMF2HI4TJMJ2XIZLTSKBKK5TBNR2WLJDUOJ2WLJDOMFWWLO3UNBZGKYLEL5YGC4TUNFRWS4DBNZ2F6YLDORUXM2LUPGBKK5TBNR2WLJDHNFZXJJDOMFWWLK3UNBZGKYLEL52HS4DFVRZXKYTKMVRXIX3UPFYGLK2HNFZXIQ3PNVWWK3TUUZ2G64DJMNZZDAVEOR4XAZNEM5UXG5FFOZQWY5LFVEYTGMBVGE4DMNBYU52HE2LHM5SXFJTDOJSWC5DF> . You are receiving this email because you authored the thread. Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub> .

Yes, I think it's a typo. A bit further down in p0=P0/Adisk, the value of E (178889) instead of P0 is written. Again, I think the correct value is used in computations.

Lars, I've been working on revising the look of Wild Peaches <https://www.wildpeaches.xyz/> over the last few months and kept thinking that I'd take another look at Stefan-Boltzmann when everything else was done because it should be an easy fix. But, now I'm wondering if the data sources were for primary energy delivered or primary energy consumed. That is, do these numbers represent useful energy to society, or total consumption? Anyway, I'll have to spend some time straightening it all out. John

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On Mon, Mar 3, 2025 at 11:11 AM Lars Ekman ***@***.***> wrote: ***@***.**** commented on this gist. ------------------------------ Yes, I think it's a typo. A bit further down in p0=P0/Adisk, the value of E (178889) instead of P0 is written. Again, I think the correct value is used in computations. — Reply to this email directly, view it on GitHub <https://gist.github.com/XerxesZorgon/6b056a34ee85fb4322053b8265f3b301#gistcomment-5466733> or unsubscribe <https://github.com/notifications/unsubscribe-auth/AC3KQPL5AQ5VFY7LF7RNZJD2SR5KRBFKMF2HI4TJMJ2XIZLTSKBKK5TBNR2WLJDUOJ2WLJDOMFWWLO3UNBZGKYLEL5YGC4TUNFRWS4DBNZ2F6YLDORUXM2LUPGBKK5TBNR2WLJDHNFZXJJDOMFWWLK3UNBZGKYLEL52HS4DFVRZXKYTKMVRXIX3UPFYGLK2HNFZXIQ3PNVWWK3TUUZ2G64DJMNZZDAVEOR4XAZNEM5UXG5FFOZQWY5LFVEYTGMBVGE4DMNBYU52HE2LHM5SXFJTDOJSWC5DF> . You are receiving this email because you authored the thread. Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub> .

do these numbers represent useful energy to society, or total consumption?

Good question, but I don't think it matters all that much. In the case of fossil fuels (~87%) it should be simple: it should be based on extraction. For example, a coal power plant may have an efficiency of 35%, but the statistics should be based on the amount of coal used, not electricity produced. And I think that's the case. Statistics on extractions should be fairly easy to get.

For wind, solar, bio and hydro, I think the stats are based on electricity produced. But they should not be included in your temperature calculations anyway, since the energy is already received by earth, just transformed to electricity.

Nuclear is trickier. I think (and I am guessing) that the stats are based on electricity produced. But a nuclear power plant has an efficiency around 35%, so the thermal effect is around 3 times the electricity output. But then again, nuclear is a small contributor (yet).

Right, I was worried that I'd gotten data that was after conversion instead of before. I'll check to be sure, but I'm hoping you're right and they're the before numbers. I also realized recently that the solar, wind and hydro values aren't strictly the electricity produced, but there's an extra loss because the systems aren't perfect. For solar, the panels reduce the albedo locally so they absorb more sunlight than would normally be taken in by the ground, and wind and hydro slow the natural flow of air and water which introduce entropy losses. I don't think it's worth correcting because the energy from these systems is minor compared to the total, but it's something to consider. Geothermal and nuclear are worse because we're extracting energy that would otherwise have remained underground for a very long time, and then it has to be radiated away.

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On Mon, Jul 7, 2025 at 1:32 AM Lars Ekman ***@***.***> wrote: ***@***.**** commented on this gist. ------------------------------ do these numbers represent useful energy to society, or total consumption? Good question, but I don't think it matters all that much. In the case of fossil fuels (~87%) it should be simple: it should be based on extraction. For example, a coal power plant may have an efficiency of 35%, but the statistics should be based on the amount of coal used, not electricity produced. And I think that's the case. Statistics on extractions should be fairly easy to get. For wind, solar, bio and hydro, I think the stats are based on electricity produced. But they should not be included in your temperature calculations anyway, since the energy is already received by earth, just transformed to electricity. Nuclear is trickier. I *think* (and I am guessing) that the stats are based on electricity produced. But a nuclear power plant has an efficiency around 35%, so the thermal effect is around 3 times the electricity output. But then again, nuclear is a small contributor (yet). — Reply to this email directly, view it on GitHub <https://gist.github.com/XerxesZorgon/6b056a34ee85fb4322053b8265f3b301#gistcomment-5665636> or unsubscribe <https://github.com/notifications/unsubscribe-auth/AC3KQPO5KICEF4YJJXZ32QT3HIA57BFKMF2HI4TJMJ2XIZLTSKBKK5TBNR2WLJDUOJ2WLJDOMFWWLO3UNBZGKYLEL5YGC4TUNFRWS4DBNZ2F6YLDORUXM2LUPGBKK5TBNR2WLJDHNFZXJJDOMFWWLK3UNBZGKYLEL52HS4DFVRZXKYTKMVRXIX3UPFYGLK2HNFZXIQ3PNVWWK3TUUZ2G64DJMNZZDAVEOR4XAZNEM5UXG5FFOZQWY5LFVEYTGMBVGE4DMNBYU52HE2LHM5SXFJTDOJSWC5DF> . You are receiving this email because you authored the thread. Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub> .