Step 2: Skip because all units are the appropriate units. Attempt them initially, and if help is needed, the solutions are right below them. There are several applications of the ideal gas law in everyday life, including determining the amount of ventilation that facilities need for safe human use and estimating proper air pressure levels in airplane cabins. Do not make the common mistake of confusing units and dimensions. 5 Values of Ideal Constant in Different Units, 7 Boltzmann's Constant and Ideal Gas Constant, 8 Gas Constant in other important equations, If you appreciate our work, consider supporting us on . Be sure to read the problem carefully, and answer what they are asking for. How do I stop the Flickering on Mode 13h? The value of R in different units is presented in the table below. A. collide more frequently with each other. What is an "ideal gas"? "Derivation of the Ideal Gas Law. Therefore, if $t$ has dimensions of time, we need to multiply it by a constant with dimensions of inverse time so that the argument is dimensionless. Infoplease is part of the Sandbox Learning family of educational and reference sites for parents, teachers and students. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. $$pV=T \tag{2}$$. An equation due to van der Waals extends the ideal gas equation in a straightforward way. The Ideal Gas Law is simply the combination of all Simple Gas Laws (Boyle's Law, Charles' Law, and Avogadro's Law), and so learning this one means that you have learned them all. and the first example, shouldn't the atm version of the ideal gas constant be 0.082 L*atm/mol*K instead of 0.082 L*atm/K? Direct link to Matt B's post No calculus needed :-) Li, Posted 7 years ago. or express from two volume/temperature points: This equation can be used to solve for initial or final value of volume or temperature under the given condition that pressure and the number of mole of the gas stay the same. Despite this fact, chemists came up with a simple gas equation to study gas behavior while putting a blind eye to minor factors. In the case of increasing/reducing the amount of gas inside, just as expected, the value of $$ will increase/reduce by the same proportion $n$ as the amount of gas added/removed. Deriving (3) for the same amount of substance, we get, $$p \mathrm{d} V+V \mathrm{d} p=nR \mathrm{d}T \tag{6}$$. He is known for his work on measurements of thermal properties of gases. The gas constant has the same unit as of entropy and molar heat capacity. Sometimes I believe that the constant is there in order to make the equation work (make the units line up per se), but other times I feel like such assumptions are unnecessary. What does the power set mean in the construction of Von Neumann universe? Don't know if that explains why it is important, but it at least explains a few things about the gas constant. Available: https://en.wikipedia.org/wiki/Gas_constant, https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_Properties_of_Matter/States_of_Matter/Properties_of_Gases/Gas_Laws/The_Ideal_Gas_Law, https://energyeducation.ca/wiki/index.php?title=Ideal_gas_constant&oldid=10541. It is defined as the ratio of the ideal gas constant to the molar gas of the gas. The ideal gas law is -. [Online]. The Ideal Gas Law may be expressed in SI units where pressure is in pascals, volume is in cubic meters, N . 1 minute = 60 seconds. k is a proportionality constant.. Assume that during an expansion against constant pressure one mole of an ideal gas does an amount of work equal to $-R\cdot \pu{1 K}\cdot\pu{1 mol} = \pu{-8.3145 J}$. The ideal gas constant is also known as the molar gas constant, the gas constant or the universal gas constant. The big leap here is a discovery by Amadeo Avogadro known as Avogadros law, which in other words, says that, if one uses the amount of substance $n$ in terms of the number of moles instead of $\mathrm{kg}$ or $\mathrm{lbs}$, then, under the same conditions of $p$ and $T$ all gases occupy the same volume, i.e., the values of the $$s are the same. It is only important if you want to relate the pressure or the volume or the moles or the temperature of a gas to any of the other values. . This constant is specific to the particular gas or mixture (hence its name), while the universal gas constant is the same for an ideal gas. When all three laws are combined into one equation, an ideal gas constant equation results; it implies the relation between four variables and describes any . Ultimately, the reason is that the atoms of an ideal gas are non-interacting point particles. After that perform a new measurement of the above parameters. Connect and share knowledge within a single location that is structured and easy to search. Now for gas constant ($R$): it is an experimental constant. *Write down all known equations: *Keeping in mind \(m=M \times n\)replace \((M \times n)\) for \(mass\) within the density formula. The theory behind the ideal gas law is that gas molecules undergo perfectly elastic (kinetic energy-conserving) collisions in a container of fixed volume, in which they take up none of the available space. When purchasing wardrobe lighting systems it's essential to carefully consider which types and features will best complement the size, shape, and electrical connection of your space; your closet size, shape, and electricity availability all play into what type of . 1 Answer. or expressed as two pressure/temperature points: Boyle's Law, Charles' Law, and Avogradro's Law and Amontons's Law are given under certain conditions so directly combining them will not work. Note that there'd be even a second constant $T_0$ to be introduced, $pV=nR(T-T_0)$ if one used Celsius or Fahrenheit for temperature, i.e., while $R$ is introduced for the "stupidity" of considering temperature as something else than energy, $T_0$ is introduced for the second "stupidity" of picking an arbitrary scale based e.g. mol-1). General Chemistry: Principles and Modern Applications. Physics questions and answers. Extracting Bases. The effect of intermolecular forces is much . If the pressure of the gas is too large (e.g. Can someone explain why this point is giving me 8.3V? Adding protein shakes to your diet is a popular way to increase protein intake. The SI unit is Jkg1K1. Where else might this constant be useful? Some of these equations are discussed below. There was really no deeper understanding about various physical processes governing the behavior of a gas. Alternatively, we could have solved this problems by using the molecular version of the ideal gas law with Boltzmann's constant to find the number of molecules first, and then converted to find the number of moles. More than 100 years later, in 1787 and again in 1802, Jacques Charles and Joseph Louis Gay-Lussac demonstrated that the temperature (T) and volume (V) of a gas also obeys a simple mathematical relationship; as temperature increases, volume increases by the same proportion implying that the ratio, V/T is constant. What is the ideal gas constant for butane? ", Levine, S. "Derivation of the Ideal Gas Law. \Large PV=nRT P V = nRT. (Eq 2) Z = a c t u a l i d e a l. They're full of billions and billions of energetic gas molecules that can collide and possibly interact with each other. or expressed from two pressure/volume points: This equation would be ideal when working with problem asking for the initial or final value of pressure or volume of a certain gas when one of the two factor is missing. E) It is a good conductor of electricity. The best answers are voted up and rise to the top, Not the answer you're looking for? (Since P is on the opposite side of the equation to n and T), Pressure, however, is indirectly proportional to volume. { "Avogadro\'s_Law" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Boyle\'s_Law" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Charles\'s_Law_(Law_of_Volumes)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Dalton\'s_Law_(Law_of_Partial_Pressures)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Gas_Laws:_Overview" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", The_Ideal_Gas_Law : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { Chemical_Reactions_in_Gas_Phase : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Gases_(Waterloo)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Gas_Laws : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Gas_Pressure : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Kinetic_Theory_of_Gases : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Properties_of_Gas : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", Real_Gases : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "showtoc:no", "license:ccbyncsa", "licenseversion:40" ], https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FPhysical_and_Theoretical_Chemistry_Textbook_Maps%2FSupplemental_Modules_(Physical_and_Theoretical_Chemistry)%2FPhysical_Properties_of_Matter%2FStates_of_Matter%2FProperties_of_Gases%2FGas_Laws%2FThe_Ideal_Gas_Law, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), Standard condition of temperature and pressure is known as, Take note of certain things such as temperature is always in its, the particles have no forces acting among them, and. It is simply a constant, and the different values of R correlates accordingly with the units given. \[\rho = \dfrac{(0.3263\; \rm{atm})(2*14.01 \; \rm{g/mol})}{(0.08206 L atm/K mol)(291 \; \rm{K})}\]. Please note that you can roll-back the edit if you want, although I would encourage careful examination of the edited version first. Combined, these form the Ideal Gas Law equation: PV = NRT. West, John B. A 3.00 L container is filled with \(Ne_{(g)}\) at 770 mmHg at 27oC. Next, Gay-Lussac's law states that temperature and pressure are proportional. Direct link to The #1 Pokemon Proponent's post That is the definition of, Posted 7 years ago. This answer contained what I believed to be several errors all related to confusion about the difference between units and dimensions. My guess is that the entropy of the nonideal gas should be greater. Boyles Law describes the inverse proportional relationship between pressure and volume at a constant temperature and a fixed amount of gas. It is a proportionality constant for the ration of #(PV)/(nT)#,where P is pressure, V is volume, n is moles of the gas, and T is the temperature in Kelvin. Take a look at the problems below for examples of each different type of problem. Even though this might seem odd, for many gases this is a very good approximation, at least at high temperatures and low densities. Temperature, kinetic theory, and the ideal gas law, [How do you convert between all these units? Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. Tikz: Numbering vertices of regular a-sided Polygon, I would like to calculate an interesting integral, Effect of a "bad grade" in grad school applications, Word order in a sentence with two clauses. Also, the specific gas constant is found in Mayer's relation. Choose any gas, assuming its ideal. 1968, 45(5), p351 DOI:10.1021/ed045p351.1. Use the Ideal Gas Equation to solve a problem when the amount of gas is given and the mass of the gas is constant. They are like symmetry points were everything moving around most do so in a way to keep their values the same. It's even a constant when it shows up in places that aren't gas laws at all! Given a constant number of mole of a gas and an unchanged volume, pressure is directly proportional to temperature. What were the poems other than those by Donne in the Melford Hall manuscript? To appreciate the distinction between curve fitting and what it means for a tool to be truly predictive it might help to consider how the ideal gas law was developed. Comment What is the partial pressure of \(CO_2\) and \(Ne\) in atm? It is used to determine the rate constant k. where A is the Arrhenius constant and Ea is the activation energy. Step 3: Plug in the variables into the appropriate equation. In this case, they are asking for temperature in Celsius, so you will need to convert it from K, the units you have. With your edit, I don't think the first bullet is true anymore. how does the K.E transfer between two molecules (elastic collision) and no loss of energy ? It is corresponding to the Boltzmann constant but articulated in units of energy per temperature . Since most gases behave more or less like an ideal gas, we of an ideal gas. For this reason, many students are taught the three most important gas laws by . Gases are complicated. The Ideal Gas Equation. 1875 (in Russian), "Mendeleef's researches on Mariotte's law 1", Individual Gas Constants and the Universal Gas Constant, https://en.wikipedia.org/w/index.php?title=Gas_constant&oldid=1149201537, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 10 April 2023, at 19:20. Notice that we plugged in the pressure in terms of, Posted 7 years ago. Solving time: 2 mins. A) It is a light gas. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Note, however, that the, Just as a formatting note, I'd recommend against using. An ideal gas can be easily characterized by three state variables: that is the absolute pressure denoted by P volume denoted by V and absolute temperature denoted by T. Ideal gas law: PV = nRT = NkT. molecules) of a gas remains the same, the quantity, This formula is particularly useful when describing an ideal gas that changes from one state to another. I have heavily edited the answer to make it correct. For those of you who haven't picked up on the idea, here's a clarification: There is no such thing as an ideal gas! The four gas variables are: pressure (P), volume (V), number of mole of gas (n), and temperature (T). 'For a given volume of a gas, as the temperature increases, the pressure of the gas is directly proportional'. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Note that for the case of the ideal gas law, it would be perfectly okay to write $PV = NT$; you would just have to understand that $T$ now means something different, i.e. Don't tell your friends, relatives, or anybody else that ideal gases are real, because they'll lock you up for being a deluded maniac! It is the ratio of the product of pressure and volume to the product of mole and temperature. [Online]. K 1) T = temperature in Kelvin. Here are the facts and trivia that people are buzzing about. In the "Units to use for PV=nRT" section, It says 1 liter=0.001 m^3=1000 cm^3. Now just convert the liters to milliliters. 6.674 08 x 10-11m3kg-1s-2 it is giving up the exact force which when two masses of 1 kg each will exert on each other when kept 1 m apart. P= Absolute Pressure (gauge pressure + atmospheric pressure) V = Volume (How much space the gas occupies) n = Mass measured in "moles" (the number of molecules) R = The universal gas constant (varies depending on the units of measure being used Example: [lb f ft/ (lb mol o R)]= 8.3145 ) For an electrochemical half-cell, the Nernst equation is. In thermodynamics, the fact that the energy of an ideal gas depends only on temperature is an experimental observation from the free expansion of a diluted gas (which is approximately ideal) 1. What factor is found in the ideal gas law which is not in the previous laws? This definition of an ideal gas contrasts with the Non-Ideal Gas definition, because this equation represents how gas actually behaves in reality. This information is summarized for convenience in the chart below. D) It has a boiling point of -252.87C. T = absolute temperature. Example: A 1.00 L flask was filled up with gas at a pressure of 751 mm Hg temperature 26C. \[ V = \dfrac{(0.25\; \rm{mol})(0.08206\; \rm{L atm}/\rm{K mol})(308\; \rm{K})}{(0.3368\; \rm{atm})}] \]. It is crucial to match your units of Pressure, Volume, number of mole, and Temperature with the units of R. How do you know the Ideal Gas Equation is the correct equation to use? temperature would have dimensions of energy, which is perfectly reasonable as described in this other post. References This airticle is a . The specific gas constant is a version of the ideal gas constant in mass form instead of molar form. What does the ideal gas law allow a scientist to calculate that the other gas laws do not. On the elasticity of gases. Now do any of the following: Heat up the gas or pull/push the piston up/down. Journal of Chemistry Education. The thermometer and the barometer are placed in such a way they can give the temperature and the pressure of the gas inside the bottle. The equation of state of n gram-moles of a perfect gas can then be written as PV/T = nR, in . This constant is written as R, and is a constant of proportionality (constant number that is multiplied on one side of a proportional relationship to make them equal) for the ideal gas law. Upper Saddle River: Pearson Education, Inc., 2007. I am purely curious of the nature of constants in cases such as $R$ (not $c$ as I understand that the speed of light is uniformly constantly) I am simply asking whether these constants are necessary for our equations and understandings or if they are universally constant. ], [Could we have used the other gas constant? It's very difficult to come up with rules for describing the behaviors of real gases because they come in a variety of different shapes and sizes, as well as experience different intermolecular forces to various degrees. 2- They multiply or add up to give the correct value of the expression ,and this value is determined by experiments. It is poisonous, greenish gas b. "Robert Boyles landmark book of 1660 with the first experiments on rarified air" Journal of Applied Physiology 98:31-39, 2005. doi: 10.1152/japplphysiol.00759.2004. Note the use of kilomoles, with the resulting factor of 1000 in the constant. Since you can't divide by 0, the formula would not work. How do you know which ideal gas constant to use? E.g. Lastly, the constant in the equation shown below is R, known as the the gas constant, which will be discussed in depth further later: minus, 200, start text, space, C, end text, R, equals, 8, point, 31, start fraction, J, divided by, K, dot, m, o, l, end fraction, start text, p, a, s, c, a, l, s, space, end text, P, a, start text, k, e, l, v, i, n, space, end text, K, R, equals, 0, point, 082, start fraction, L, dot, a, t, m, divided by, K, dot, m, o, l, end fraction, start text, a, t, m, o, s, p, h, e, r, e, s, space, end text, a, t, m, start text, l, i, t, e, r, s, space, end text, L, N, start text, space, n, u, m, b, e, r, space, o, f, space, m, o, l, e, c, u, l, e, s, end text, n, start text, space, m, o, l, e, s, end text, P, V, equals, N, k, start subscript, B, end subscript, T, k, start subscript, B, end subscript, equals, 1, point, 38, times, 10, start superscript, minus, 23, end superscript, start fraction, J, divided by, K, end fraction, start text, p, a, s, c, a, l, s, space, P, a, end text, start text, k, e, l, v, i, n, space, K, end text, n, R, equals, N, k, start subscript, B, end subscript, equals, start fraction, P, V, divided by, T, end fraction, equals, start text, space, c, o, n, s, t, a, n, t, end text, start fraction, P, V, divided by, T, end fraction, start fraction, P, start subscript, 1, end subscript, V, start subscript, 1, end subscript, divided by, T, start subscript, 1, end subscript, end fraction, equals, start fraction, P, start subscript, 2, end subscript, V, start subscript, 2, end subscript, divided by, T, start subscript, 2, end subscript, end fraction, 1, point, 54, start text, space, a, t, m, end text, 0, point, 119, start text, space, m, end text, 25, start superscript, o, end superscript, start text, space, C, end text, (usethemolarformoftheidealgaslaw), P, V, equals, n, R, T, start text, left parenthesis, u, s, e, space, t, h, e, space, m, o, l, a, r, space, f, o, r, m, space, o, f, space, t, h, e, space, i, d, e, a, l, space, g, a, s, space, l, a, w, right parenthesis, end text, n, equals, start fraction, P, V, divided by, R, T, end fraction, start text, left parenthesis, s, o, l, v, e, space, f, o, r, space, t, h, e, space, n, u, m, b, e, r, space, o, f, space, m, o, l, e, s, right parenthesis, end text, (decidewhichgasconstantwewanttouse), n, equals, start fraction, P, V, divided by, left parenthesis, 8, point, 31, start fraction, J, divided by, K, dot, m, o, l, end fraction, right parenthesis, T, end fraction, start text, left parenthesis, d, e, c, i, d, e, space, w, h, i, c, h, space, g, a, s, space, c, o, n, s, t, a, n, t, space, w, e, space, w, a, n, t, space, t, o, space, u, s, e, right parenthesis, end text, start text, p, a, s, c, a, l, s, end text, 1, point, 54, start text, space, a, t, m, end text, times, left parenthesis, start fraction, 1, point, 013, times, 10, start superscript, 5, end superscript, start text, space, P, a, end text, divided by, 1, start text, space, a, t, m, end text, end fraction, right parenthesis, equals, 156, comma, 000, start text, space, P, a, end text, start fraction, 4, divided by, 3, end fraction, pi, r, cubed, V, equals, start fraction, 4, divided by, 3, end fraction, pi, r, cubed, equals, start fraction, 4, divided by, 3, end fraction, pi, left parenthesis, 0, point, 119, start text, space, m, end text, right parenthesis, cubed, equals, 0, point, 00706, start text, space, m, end text, cubed, T, start subscript, K, end subscript, equals, T, start subscript, C, end subscript, plus, 273, start text, space, K, end text, T, equals, 25, start superscript, o, end superscript, start text, space, C, end text, plus, 273, start text, space, K, end text, equals, 298, start text, space, K, end text, (plugincorrectunitsforthisgasconstant), n, equals, start fraction, left parenthesis, 156, comma, 000, start text, space, P, a, end text, right parenthesis, left parenthesis, 0, point, 00706, start text, space, m, end text, cubed, right parenthesis, divided by, left parenthesis, 8, point, 31, start fraction, J, divided by, K, dot, m, o, l, end fraction, right parenthesis, left parenthesis, 298, start text, space, K, end text, right parenthesis, end fraction, start text, left parenthesis, p, l, u, g, space, i, n, space, c, o, r, r, e, c, t, space, u, n, i, t, s, space, f, o, r, space, t, h, i, s, space, g, a, s, space, c, o, n, s, t, a, n, t, right parenthesis, end text, n, equals, 0, point, 445, start text, space, m, o, l, e, s, end text, start text, m, o, l, e, c, u, l, e, s, end text, N, equals, 0, point, 445, start text, space, m, o, l, e, s, end text, times, left parenthesis, start fraction, 6, point, 02, times, 10, start superscript, 23, end superscript, start text, space, m, o, l, e, c, u, l, e, s, end text, divided by, 1, start text, space, m, o, l, e, end text, end fraction, right parenthesis, equals, 2, point, 68, times, 10, start superscript, 23, end superscript, start text, space, m, o, l, e, c, u, l, e, s, end text, T, equals, 293, start text, space, K, end text, T, equals, 255, start text, space, K, end text, 255, start text, space, K, end text, point, (startwiththeproportionalversionoftheidealgaslaw), start fraction, P, start subscript, 1, end subscript, V, start subscript, 1, end subscript, divided by, T, start subscript, 1, end subscript, end fraction, equals, start fraction, P, start subscript, 2, end subscript, V, start subscript, 2, end subscript, divided by, T, start subscript, 2, end subscript, end fraction, start text, left parenthesis, s, t, a, r, t, space, w, i, t, h, space, t, h, e, space, p, r, o, p, o, r, t, i, o, n, a, l, space, v, e, r, s, i, o, n, space, o, f, space, t, h, e, space, i, d, e, a, l, space, g, a, s, space, l, a, w, right parenthesis, end text, (volumeisthesamebeforeandaftersincethecanisterisrigid), start fraction, P, start subscript, 1, end subscript, V, divided by, T, start subscript, 1, end subscript, end fraction, equals, start fraction, P, start subscript, 2, end subscript, V, divided by, T, start subscript, 2, end subscript, end fraction, start text, left parenthesis, v, o, l, u, m, e, space, i, s, space, t, h, e, space, s, a, m, e, space, b, e, f, o, r, e, space, a, n, d, space, a, f, t, e, r, space, s, i, n, c, e, space, t, h, e, space, c, a, n, i, s, t, e, r, space, i, s, space, r, i, g, i, d, right parenthesis, end text, start fraction, P, start subscript, 1, end subscript, divided by, T, start subscript, 1, end subscript, end fraction, equals, start fraction, P, start subscript, 2, end subscript, divided by, T, start subscript, 2, end subscript, end fraction, start text, left parenthesis, d, i, v, i, d, e, space, b, o, t, h, space, s, i, d, e, s, space, b, y, space, end text, V, right parenthesis, P, start subscript, 2, end subscript, equals, T, start subscript, 2, end subscript, start fraction, P, start subscript, 1, end subscript, divided by, T, start subscript, 1, end subscript, end fraction, start text, left parenthesis, s, o, l, v, e, space, f, o, r, space, t, h, e, space, p, r, e, s, s, u, r, e, space, end text, P, start subscript, 2, end subscript, right parenthesis, (pluginvaluesforpressureandtemperature, P, start subscript, 2, end subscript, equals, left parenthesis, 255, start text, space, K, end text, right parenthesis, start fraction, 1, start text, space, a, t, m, end text, divided by, 293, start text, space, K, end text, end fraction, start text, left parenthesis, p, l, u, g, space, i, n, space, v, a, l, u, e, s, space, f, o, r, space, p, r, e, s, s, u, r, e, space, a, n, d, space, t, e, m, p, e, r, a, t, u, r, e, end text, right parenthesis, P, start subscript, 2, end subscript, equals, 0, point, 87, start text, space, a, t, m, end text, start text, left parenthesis, c, a, l, c, u, l, a, t, e, space, a, n, d, space, c, e, l, e, b, r, a, t, e, end text, right parenthesis, start text, a, t, m, o, s, p, h, e, r, e, s, end text, P, start subscript, 2, end subscript, equals, 0, point, 87, start text, space, a, t, m, end text, times, left parenthesis, start fraction, 1, point, 013, times, 10, start superscript, 5, end superscript, start text, space, P, a, end text, divided by, 1, start text, space, a, t, m, end text, end fraction, right parenthesis, equals, 88, comma, 200, start text, space, P, a, end text, start text, left parenthesis, c, o, n, v, e, r, t, space, f, r, o, m, space, a, t, m, o, s, p, h, e, r, e, s, space, t, o, space, p, a, s, c, a, l, s, end text, right parenthesis. 2022 Sandbox Networks Inc. 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