{"id":78,"date":"2020-12-06T17:30:24","date_gmt":"2020-12-07T00:30:24","guid":{"rendered":"https:\/\/web.siei.org\/?page_id=78"},"modified":"2020-12-06T17:30:24","modified_gmt":"2020-12-07T00:30:24","slug":"useful-equations","status":"publish","type":"page","link":"https:\/\/www.siei.org\/?page_id=78","title":{"rendered":"Useful Equations"},"content":{"rendered":"\n<p>It can be hard to track the various measures used for hydrogen systems. Below are some conversions and definitions:<\/p>\n\n\n\n<p><strong>STP = standard temperature\/pressure = 0\u00b0C (32\u00b0f) and 1 bar (\u22481 atmosphere).<\/strong>But: Some references say STP is 25\u00b0C (77\u00b0f). We do not understand this discrepancy.<\/p>\n\n\n\n<p>NTP = normal temperature\/pressure = 20\u00b0C (68\u00b0f) and 1 atm (atmosphere). Functionally, NTP is almost the same as STP , and STP is more common.<\/p>\n\n\n\n<p><strong>1 atm = 1 atmosphere = 14.7 psi.<\/strong><\/p>\n\n\n\n<p><strong>scf = &#8220;scuff&#8221; = standard cubic foot = 1 c.f. (STP).<\/strong><\/p>\n\n\n\n<p>ncf = normal cubic foot = 1 c.f. (NTP).<\/p>\n\n\n\n<p><strong>1 gallon = 3.78 liters<\/strong><\/p>\n\n\n\n<p><strong>1 cubic foot = 7.5 gallons = 28.25 liters.<\/strong><\/p>\n\n\n\n<p>1 liter = 1000 cc (cubic centimeters).<\/p>\n\n\n\n<p>1 kilogram = 1kg = 1000 grams.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>The Ideal Gas Law: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<u>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Pressure x Volume&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/u>&nbsp;= &nbsp;&nbsp;<u>PV<\/u>&nbsp; = &nbsp;constant.<\/strong><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;no. of atoms x Temperature&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; nT<\/strong>&nbsp;In practice we have temperature and volume both constant. &#8220;No. of atoms&#8221; is equivalent to &#8220;amount of gas&#8221;.&nbsp;<strong>The Gas Law says that for fixed volume, if we double (or triple etc) the pressure we double (or triple etc) the amount of gas. This is an awesome result.<\/strong>&nbsp;For example, a 60 cubic foot tank filled to 200 psi (14 atm) contains about 60 x 14 = 840 scf of gas.This equality is accurate for hydrogen (and most gases) to within 2% up to 30 atm (\u2248450 psi). Even at higher pressures, say 3000 psi, the Gas Law is accurate to within 15-20% for hydrogen (it predicts a bit low). Temperature is in degrees Kelvin, so it&#8217;s effectively constant: Because 0\u00b0 C = 273\u00b0 K, and 20\u00b0 C = 293\u00b0 K, the ratio of two real-life Kelvin temperatures is always close to 1, and thus does not affect the equation.<\/p>\n\n\n\n<p><strong>A K-cylinder holds about 1 cubic foot. The scf it holds will vary with the gas and the company.<\/strong><strong>&nbsp;A K-cylinder of hydrogen (at 2500 psi) holds roughly 200 scf. A K-cylinder of nitrogen (at 3000 psi) holds roughly 250 scf.<\/strong>&nbsp;(Note that these figures are higher than the Gas Law predicts.)<\/p>\n\n\n\n<p>A&nbsp;<strong>mole<\/strong>&nbsp;is a certain amount of stuff, defined as 6 x 10<sup>23<\/sup>&nbsp;molecules of the compound (Avagadro&#8217;s number). The mass of 1 mole of a compound is equal to its atomic weight, in grams. For example, 1 mole of water (H<sub>2<\/sub>O) has 2 x 1 + 16 = 18 grams mass.<\/p>\n\n\n\n<p><strong>Avagadro&#8217;s Law:<\/strong>&nbsp;<strong>The volume of 1 mole of&nbsp;<u>any<\/u>&nbsp;gas (stp) = 22.4 liters. This is an amazing, useful result.<\/strong><\/p>\n\n\n\n<p><strong>Mass of 1 mole hydrogen gas (H<sub>2<\/sub>) = 2 grams. So the mass of 22.4 liters (stp) H<sub>2<\/sub>&nbsp;is 2 g.<\/strong>Mass of 1 mole nitrogen gas (N<sub>2<\/sub>) =28 g.Mass of 1 mole oxygen gas (O<sub>2<\/sub>) = 32 g.Mass of 1 mole air \u2248 29 g.Mass of 1 mole propane (C<sub>3<\/sub>H<sub>8<\/sub>) = 44 g.Mass of 1 mole natural gas (mostly methane, CH<sub>4<\/sub>) \u2248 16 g.Mass of 1 mole gasoline (C<sub>8<\/sub>H<sub>18<\/sub>) = 114 g.<\/p>\n\n\n\n<p>Air \u2248 78% nitrogen, 21% oxygen, 1% other (argon, particulates,,water vapor), 0.03% CO<sub>2<\/sub>(!).<\/p>\n\n\n\n<p>Avagadro&#8217;s Law also implies that for gases at equal pressure and temperature, proportions of volume are the same as proportions of amount of gas. For example, 1 cc of H<sub>2<\/sub>&nbsp;mixed with 1 liter of air gives a 0.1%, or 1000 ppm, concentration of H<sub>2<\/sub>.<\/p>\n\n\n\n<p>____________________<\/p>\n\n\n\n<p><strong>Amps x Volts = Watts.&nbsp;<\/strong>For example, a 100 watt bulb draws 0.83 amps at 120 volts.<\/p>\n\n\n\n<p><strong><em>Joule, Watt-hour, Btu<\/em>&nbsp;and&nbsp;<em>calorie<\/em>&nbsp;are all units of energy. Watt-hours are the most convenient unit for electric systems.<\/strong><\/p>\n\n\n\n<p><strong>1 Watt = 1 Joule\/second. So 1 Watt-hour = 3.6 kJ.<\/strong>&nbsp;This is the most relevant conversion.<\/p>\n\n\n\n<p>1 kW = 1 kilowatt = 1000 watts.<\/p>\n\n\n\n<p>1 Btu \u2248 1 kJ = 1 kiloJoule = 1000 J.<\/p>\n\n\n\n<p>1 calorie = 4.184 J. &nbsp;&nbsp;&nbsp;&nbsp;(Aside: A &#8220;calorie&#8221; as used for food energy is actually a kilocalorie, or 1000 calories, so an english muffin contains 130,000 calories, = 130 &#8220;calories&#8221;.)<\/p>\n\n\n\n<p><strong>Energy storage of a lead-acid L-16 battery: 350 amp-hours @ 6 volts =2100 Wh. nominal. Effective (usable) energy is half, ie about 1 kWh.<\/strong>&nbsp;The usable storage is less because draining batteries beyond about half shortens their lifespan drastically.<\/p>\n\n\n\n<p><strong>Energy Density of H<sub>2&nbsp;<\/sub>(STP) = 3.2 &#8211; 3.5 Watt-hours\/liter.<\/strong>&nbsp;The figure can be calculated different ways (in particular,assuming different temperatures), giving different results.<strong>Energy released by combustion of H<sub>2<\/sub>&nbsp;= 242 kJ\/mole.<\/strong>&nbsp;This is the energy released in the reaction H<sub>2<\/sub>&nbsp;+ \u00bd O<sub>2<\/sub>&nbsp;\u2192 H<sub>2<\/sub>O (steam) + heat. In a fuel cell, part of this energy is electrical, part is heat. Compare natural gas (800 kJ\/mole) and gasoline (5500 kJ\/mole).Per kilogram, H<sub>2<\/sub>&nbsp;stores more energy because a mole of H<sub>2<\/sub>&nbsp;weighs so much less. But 242 kJ of H<sub>2<\/sub>&nbsp;takes up the same volume (= 22.4 liters, stp) as 800 kJ of natural gas. Gasoline, because it is a liquid, is much more dense- 22.4 liters of gasoline is roughly 160 moles, containing 900,000 kJ of energy! It is more energy-dense than dynamite. One can readily see why our civilization has become so dependent on oil- it is miraculous stuff. But hydrogen is miraculous too, in different ways.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It can be hard to track the various measures used for hydrogen systems. Below are some conversions and definitions: STP = standard temperature\/pressure = 0\u00b0C (32\u00b0f) and 1 bar (\u22481 atmosphere).But: Some references say STP is 25\u00b0C (77\u00b0f). We do not understand this discrepancy. NTP = normal temperature\/pressure = 20\u00b0C (68\u00b0f) and 1 atm (atmosphere). &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.siei.org\/?page_id=78\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Useful Equations&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www.siei.org\/index.php?rest_route=\/wp\/v2\/pages\/78"}],"collection":[{"href":"https:\/\/www.siei.org\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.siei.org\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.siei.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.siei.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=78"}],"version-history":[{"count":1,"href":"https:\/\/www.siei.org\/index.php?rest_route=\/wp\/v2\/pages\/78\/revisions"}],"predecessor-version":[{"id":79,"href":"https:\/\/www.siei.org\/index.php?rest_route=\/wp\/v2\/pages\/78\/revisions\/79"}],"wp:attachment":[{"href":"https:\/\/www.siei.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=78"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}