{"product_id":"boltzmanns-stone-counting-w-plate-012-physics-poster","title":"Boltzmann's Stone: Counting W – Plate 012 Physics Poster","description":"\u003cp\u003ePlate 12 speaks for itself: \u003cem\u003e“Three boxes, three quanta, ten ways.”\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eEntropy counts microstates. Three identical quanta shared among three distinguishable boxes can be arranged in C(5,2) = 10 ways.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eS = k_B ln W\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eS: entropy, J K⁻¹\u003c\/li\u003e\n\u003cli\u003ek_B: Boltzmann constant, 1.380649×10⁻²³ J K⁻¹ (exact)\u003c\/li\u003e\n\u003cli\u003eW: number of microstates, dimensionless\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eq = 3: 3+0+0 (3 ways), 2+1+0 (6 ways), 1+1+1 (1 way) = 10.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The formula is engraved on Boltzmann's tombstone in Vienna; the k_B notation is Planck's.\u003c\/p\u003e\u003ch3\u003eSources\u003c\/h3\u003e\u003cul\u003e\n\u003cli\u003eL. Boltzmann, Wien. Ber. 76, 373 (1877).\u003c\/li\u003e\n\u003cli\u003eSI Brochure, 9th ed. (2019): exact k_B.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch3\u003eOn the poster\u003c\/h3\u003e\u003cp\u003ePlate 012, “Boltzmann's Stone: Counting W”: the pixel-art plate with its slogan “Three boxes, three quanta, ten ways.”, 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":50961623449703,"sku":"23504450528216341533","price":19.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Fine Art","offer_id":50961623482471,"sku":"50240025266664698676","price":29.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Semi Glossy","offer_id":50961623515239,"sku":"29581173353392648386","price":19.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Fine Art","offer_id":50961623548007,"sku":"45733940748421317577","price":44.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Semi Glossy","offer_id":50961623580775,"sku":"19483973371327342245","price":29.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Matte","offer_id":50961623613543,"sku":"34025907388617394967","price":29.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Matte","offer_id":50961623646311,"sku":"11745752542392037182","price":69.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Fine Art","offer_id":50961623679079,"sku":"32801375546375907710","price":119.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Semi Glossy","offer_id":50961623711847,"sku":"25593526633841972064","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/2027714781197481094_2048.jpg?v=1793632310","url":"https:\/\/pixelatedphysics.com\/zh-hant\/products\/boltzmanns-stone-counting-w-plate-012-physics-poster","provider":"Pixelated Physics","version":"1.0","type":"link"}