Keith Mack
The ideal gas law demonstrates the relationship between temperature, pressure, and volume for gases. The equation is PV=nRT, where P is pressure, V is volume, T is temperature, n is the number of moles of gas, and R is the universal gas constant. The temperature value in the ideal gas law must be in absolute units, either Rankine (°R) or Kelvin (K). The Rankine scale uses a different unit of measurement, where 1 degree Rankine (°R) is equal to one degree Fahrenheit. The ideal gas constant, R, is a physical constant that relates the properties of an ideal gas to its temperature, volume, and pressure. The value of R will differ depending on the scale being used, and it is important to ensure that the units of temperature are consistent when using the ideal gas constant in calculations.
| Characteristics | Values |
|---|---|
| Temperature unit in the ideal gas law | Must be in absolute units, either Rankine (°R) or Kelvin (K) |
| Conversion formula from Rankine to Kelvin | K = (°R + 459.67) x 5/9 |
| Ideal gas constant for air in imperial units | R = 1716 ftlbf/slug°R |
| Ideal gas constant for air in SI units | R = 0.287 kJ/kg*K |
| Ideal gas law equation | PV=nRT |
| Where: | P = pressure, V = volume, n = number of moles of gas, R = universal gas constant, T = absolute temperature |
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What You'll Learn
The ideal gas law equation
The ideal gas law is an equation that demonstrates the relationship between temperature, pressure, and volume for gases. It is a combination of Charles's, Boyle's, and Gay-Lussac's laws. Charles's law identifies the direct proportionality between volume and temperature at constant pressure. Boyle's law identifies the inverse proportionality of pressure and volume at a constant temperature, and Gay-Lussac's law identifies the direct proportionality of pressure and temperature at a constant volume.
The ideal gas law also holds for a system containing multiple ideal gases, known as an ideal gas mixture. With multiple ideal gases in a system, these particles are assumed to have no intermolecular interactions with one another and meet all criteria of an ideal gas law independently. An ideal gas mixture partitions the system's total pressure into the partial pressure contributions of each gas particle. Consequently, the previous ideal gas equation can be rewritten as PiV=niRT, where Pi is the partial pressure of species i and ni are the moles of species i.
The ideal gas law is a good approximation of the behaviour of many gases under many conditions, although it has several limitations. It neglects both molecular size and intermolecular attractions, so it is most accurate for monatomic gases at high temperatures and low pressures. The relative importance of intermolecular attractions diminishes with increasing thermal kinetic energy, i.e., with increasing temperatures.
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Converting between temperature scales
Temperature scales are used to measure the hotness or coldness of an object or environment. The three most common temperature scales are Celsius, Fahrenheit, and Kelvin. Each scale has its own set of reference points and intervals, so it is sometimes necessary to convert between them. For example, water freezes at 0°C or 32°F, and boils at 100°C or 212°F. Normal human body temperature is typically stated as 37°C or 98.6°F, but the more precise conversion is 36.8°C or 98.2°F.
The Fahrenheit scale was developed by Polish-German physicist and engineer Daniel Gabriel Fahrenheit in 1724. Fahrenheit created the mercury-in-glass thermometer, which was more accurate than previous thermometers. He defined zero degrees on the Fahrenheit scale as the temperature of a mixture of ice and salt, and 100 degrees as the average human body temperature.
The Celsius scale, on the other hand, was proposed by Swedish astronomer and physicist Anders Celsius in the 18th century. Celsius suggested a scale with 0 degrees as the freezing point of water and 100 degrees as the boiling point. Today, Celsius is the most widely used temperature scale globally.
The Kelvin scale, also known as the absolute temperature scale, was conceived by William Thomson, or Lord Kelvin, in collaboration with other physicists. Kelvin proposed the idea of an absolute temperature scale based on absolute zero, where molecular motion ceases. This scale is invaluable in scientific research and engineering as it provides a universal reference point independent of the properties of specific materials.
Other temperature scales include the Réaumur scale, named after René-Antoine Ferchault de Réaumur, which was once widely used in parts of Europe, particularly France and Germany. It divided the temperature range between the freezing and boiling points of water into 80 equal parts, with the freezing point as 0 degrees Réaumur and the boiling point as 80 degrees Réaumur. Today, it is used in some European cheese factories and in the Netherlands for cooking sugar syrup.
When using the ideal gas law, the temperature value must be in absolute units, either Rankine (°R) or Kelvin (K). The Rankine scale is used in the ideal gas law equation, where P (pressure) is measured in psia, V (volume) is in cubic feet, n (number of moles of gas) is in pound-moles, and R (gas constant) is 10.7316 cubic feet-psia per lb-moles-degree Rankine. To convert from Fahrenheit (F) or Celsius (C) to absolute temperature units, a fixed value is added: °R=F+459.67 and K=C+273.15.
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Units of measurement
The ideal gas law demonstrates the relationship between temperature, pressure, and volume for gases. The equation for this is PV=nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant, and T is the absolute temperature.
The universal gas constant R is a number that satisfies the proportionalities of the pressure-volume-temperature relationship. R has different values and units that depend on the pressure, volume, moles, and temperature specifications. The temperature value in the ideal gas law must be in absolute units, either Rankine (°R) or Kelvin (K). This is because, if the temperature is not in absolute units, the right-hand side of the equation could be zero, which violates the pressure-volume-temperature relationship.
The Rankine scale uses a different unit of measurement to other scales – the degree Rankine (°R) – which is equal to one degree Fahrenheit. This means that the Rankine scale has the same intervals as the Fahrenheit scale, but with a different zero point. The zero point for the Rankine scale is absolute zero, similar to the Kelvin scale. The ideal gas constant, R, can be used in calculations involving gases on any temperature scale, but the value of R will differ depending on the scale being used.
The ideal gas constant for air is often given in imperial units as R = 1716 ft*lbf/slug*°R, where 1 ft*lbf = 1.356x10^-3 kJ, 1 slug = 14.59 kg, and °R = 9/5K. This can be converted to R = 0.0886 kJ/kg*K.
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The universal gas constant
The value of the universal gas constant is dependent on the units used for pressure, volume, moles, and temperature. For example, in the imperial system, the most common units for the individual gas constant are ft lb/slugoR, while in the SI system, the most common units are J/kg K. The SI value of the molar gas constant is considered exact due to the definition of NA and k in SI units. The universal gas constant can be calculated as the product of the individual gas constant for a particular gas and the molecular weight of that gas.
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Ideal gas mixtures
The ideal gas law assumes that all gases behave identically and that their behaviour is independent of attractive and repulsive forces. This law can be used for a system containing multiple ideal gases, known as an ideal gas mixture.
In an ideal gas mixture, the system's total pressure is partitioned into the partial pressure contributions of each gas particle. The ideal gas equation can be rewritten as: PiV=niRT, where Pi is the partial pressure of species i and ni are the moles of species i. The total pressure exerted by a mixture of gases is the sum of the partial pressures of each gas. This is known as Dalton's law of partial pressures.
The universal gas constant, R, is a number that satisfies the proportionalities of the pressure-volume-temperature relationship. The temperature value in the ideal gas law must be in absolute units, either Rankine (°R) or Kelvin (K). This is because, without this, the right-hand side of the equation would be zero, which violates the pressure-volume-temperature relationship.
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Frequently asked questions
Yes, the Ideal Gas Law requires the use of absolute temperature units, such as degrees Rankine (°R) or Kelvin (K). The temperature value in the equation must be in one of these absolute units to prevent the right-hand side of the equation from being zero, which would violate the pressure-volume-temperature relationship.
The Ideal Gas Law is an equation that demonstrates the relationship between temperature, pressure, and volume for gases. It is derived from Charles's, Boyle's, and Gay-Lussac's laws. The equation is PV=nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the universal gas constant, and T is the absolute temperature.
The universal gas constant, also known as the gas constant, molar gas constant, or ideal gas constant, is denoted by the symbol R or R. It is a physical constant that relates the properties of an ideal gas to its temperature, volume, and pressure. The constant is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation.
