{"product_id":"debyes-t-plate-060-physics-poster","title":"Debye's T³ – Plate 060 Physics Poster","description":"\u003cp\u003ePlate 60 speaks for itself: \u003cem\u003e“Forget heat.”\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eAt room temperature a solid's heat capacity is about 3R per mole (Dulong–Petit). Far below the Debye temperature only long-wavelength vibrations are excited and the heat capacity falls as T³.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eC_V = (12π⁴\/5) N k_B (T\/Θ_D)³\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eC_V: heat capacity at constant volume, J K⁻¹\u003c\/li\u003e\n\u003cli\u003eN: number of atoms, dimensionless\u003c\/li\u003e\n\u003cli\u003ek_B: Boltzmann constant, J K⁻¹\u003c\/li\u003e\n\u003cli\u003eT: temperature, K\u003c\/li\u003e\n\u003cli\u003eΘ_D: Debye temperature (Cu ≈ 343 K), K\u003c\/li\u003e\n\u003cli\u003eR: gas constant 8.314 J mol⁻¹ K⁻¹\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eRoom temperature: about 3R per mole. Far below Θ_D it falls as T³.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e In metals the electrons add a term linear in T that wins at the lowest temperatures.\u003c\/p\u003e\u003ch3\u003eSources\u003c\/h3\u003e\u003cul\u003e\n\u003cli\u003eP. Debye, Ann. Phys. 344, 789 (1912).\u003c\/li\u003e\n\u003cli\u003eC. Kittel, Introduction to Solid State Physics, 8th ed., Ch. 5.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch3\u003eOn the poster\u003c\/h3\u003e\u003cp\u003ePlate 060, “Debye's T³”: the pixel-art plate with its slogan “Forget heat.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"9'' x 12\" (Vertical) \/ Matte","offer_id":50962559696999,"sku":"12627622759900718144","price":19.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Fine Art","offer_id":50962559729767,"sku":"21398358850897537239","price":29.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Semi Glossy","offer_id":50962559762535,"sku":"17340957448166833465","price":19.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Fine Art","offer_id":50962559795303,"sku":"26112128900612492306","price":44.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Semi Glossy","offer_id":50962559828071,"sku":"23338251576738752857","price":29.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Matte","offer_id":50962559860839,"sku":"24786577143455662890","price":29.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Matte","offer_id":50962559893607,"sku":"55022465873713353825","price":69.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Fine Art","offer_id":50962559926375,"sku":"61893164856346565261","price":119.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Semi Glossy","offer_id":50962559959143,"sku":"28743275046585478012","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/16599978079865235209_2048.jpg?v=1793634956","url":"https:\/\/pixelatedphysics.com\/fr\/products\/debyes-t-plate-060-physics-poster","provider":"Pixelated Physics","version":"1.0","type":"link"}