{"product_id":"kelvinor-kelvins-age-of-the-earth-physics-t-shirt","title":"Kelvinor – Kelvin's Age of the Earth Physics T-Shirt","description":"\u003cp\u003eKelvinor raises his thermometer sword over an Earth far older than he thinks.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn 1862 William Thomson, later Lord Kelvin, treated the Earth as a body that began molten and has cooled by conduction alone. From the measured rise of temperature with depth, a starting temperature and the rock's diffusivity, the half-space conduction solution gives an age. He bracketed it between 20 and 400 million years.\u003c\/p\u003e\u003cp\u003eThe model left out heat carried by convection inside the Earth (John Perry argued in 1895 that a more conductive interior gives far larger ages) and radioactive heating, discovered after 1896. In 1956 Clair Patterson, using lead isotopes in meteorites, found 4.55 ± 0.07 billion years.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003et ≈ T₀² \/ (π κ G²)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003et: age (s)\u003c\/li\u003e\n\u003cli\u003eT₀: starting temperature (K)\u003c\/li\u003e\n\u003cli\u003eκ: rock thermal diffusivity (m²\/s)\u003c\/li\u003e\n\u003cli\u003eG: surface temperature gradient (K\/m)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThomson, “On the secular cooling of the earth”, Trans. R. Soc. Edinb. 23, 157 (read 1862); Perry, Nature 51, 224 (1895); Patterson, Geochim. Cosmochim. Acta 10, 230 (1956).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Radioactivity alone did not fix the estimate; convection mattered at least as much. His conduction mathematics was sound; the model was missing pieces.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Kelvinor, the pixel-art character, with “FAR TOO YOUNG”. Back: the conduction-only age formula, Kelvin's 1862 range, the missing convection and radioactive heat, and Patterson's 1956 age. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50960519987303,"sku":"38152880305163227318","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50960520020071,"sku":"22865670912471627545","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50960520052839,"sku":"14126413799263934110","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50960520085607,"sku":"10349868855698064846","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50960520118375,"sku":"10020520094731989603","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50960520151143,"sku":"14343867918262661857","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50960520183911,"sku":"33836181557981420755","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50960520216679,"sku":"38604346501177418480","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50960520249447,"sku":"33335560729349206641","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50960520282215,"sku":"68347281462401269908","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50960520314983,"sku":"11610267668228701137","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50960520347751,"sku":"17781966412096116902","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50960520380519,"sku":"16258964964788816427","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50960520413287,"sku":"22349740258337196479","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50960520446055,"sku":"65200758608949616005","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50960520478823,"sku":"21545522155610391258","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/kelvin-age-of-earth_front_01_white.png?v=1793625793","url":"https:\/\/pixelatedphysics.com\/es\/products\/kelvinor-kelvins-age-of-the-earth-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}