{"product_id":"paschens-curve-plate-080-physics-poster","title":"Paschen's Curve – Plate 080 Physics Poster","description":"\u003cp\u003ePlate 80 speaks for itself: \u003cem\u003e“There's an easiest way for air to break.”\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eThe voltage to spark across a gap depends on the product of pressure and gap. Too little gas and electrons make too few collisions; too much and they cannot gain enough energy. In between is a minimum.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eV_b = B pd \/ (ln(A pd) − C)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eV_b: breakdown voltage, V\u003c\/li\u003e\n\u003cli\u003ep: pressure, Pa (quoted in Torr)\u003c\/li\u003e\n\u003cli\u003ed: gap, m (quoted in cm)\u003c\/li\u003e\n\u003cli\u003eA, B: gas constants\u003c\/li\u003e\n\u003cli\u003eC: ln(1 + 1\/γ), dimensionless\u003c\/li\u003e\n\u003cli\u003eγ: secondary electron emission coefficient, dimensionless\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eC = ln(1 + 1\/γ); γ: secondary emission. Air (tabulated): ≈ 327 V at pd ≈ 0.57 Torr·cm.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The minimum depends on electrode material and conditions; 327 V is a typical tabulated value for air.\u003c\/p\u003e\u003ch3\u003eSources\u003c\/h3\u003e\u003cul\u003e\n\u003cli\u003eF. Paschen, Ann. Phys. 273, 69 (1889).\u003c\/li\u003e\n\u003cli\u003eY. P. Raizer, Gas Discharge Physics (1991).\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch3\u003eOn the poster\u003c\/h3\u003e\u003cp\u003ePlate 080, “Paschen's Curve”: the pixel-art plate with its slogan “There's an easiest way for air to break.”, 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":50962681299047,"sku":"29984670748477816326","price":19.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Fine Art","offer_id":50962681331815,"sku":"86658182476144504842","price":29.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Semi Glossy","offer_id":50962681364583,"sku":"28392782269211275567","price":19.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Fine Art","offer_id":50962681397351,"sku":"23643894584347197000","price":44.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Semi Glossy","offer_id":50962681430119,"sku":"50520551552027199538","price":29.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Matte","offer_id":50962681462887,"sku":"79654187336634898027","price":29.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Matte","offer_id":50962681495655,"sku":"15402303965812760712","price":69.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Fine Art","offer_id":50962681528423,"sku":"30996219074052431087","price":119.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Semi Glossy","offer_id":50962681561191,"sku":"64810696286238831860","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/18228845178142449089_2048.jpg?v=1793636698","url":"https:\/\/pixelatedphysics.com\/es\/products\/paschens-curve-plate-080-physics-poster","provider":"Pixelated Physics","version":"1.0","type":"link"}