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The gas laws, including Charles's Law, Avogadro's Law, Boyle's Law, and Amonton's Law, are typically expressed using the Kelvin temperature scale rather than the Celsius scale. This is because the Kelvin scale is absolute, whereas the Celsius scale is arbitrary, with negative values possible. Gas laws require temperature to be calculated on an absolute scale, and so Kelvin is used. However, standard temperature and pressure (STP) is defined as 0°C, and so this value is used in the Ideal Gas Law, although it must be converted to Kelvin when plugging it into the equation.
| Characteristics | Values |
|---|---|
| Gas laws use Kelvin instead of Celsius because | Kelvin is an absolute scale, whereas Celsius is arbitrary. |
| On the Kelvin scale, 0 is absolute zero, the coldest matter can be. | |
| Negative degrees are possible with Celsius, which may cause confusing results. | |
| Temperature is always in its SI units of Kelvin (K) rather than Celsius (C) when using the Ideal Gas Equation. | |
| Gas constant R changes when dealing with different units of pressure and volume. | |
| Gas constant R is calculated depending on p, n, and the gas constant R. | |
| Charles' Law, which describes the relationship between volume and temperature, does not work with Celsius. |
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What You'll Learn
- Gas laws use Kelvin, not Celsius, because Kelvin is an absolute scale
- Celsius is arbitrary and can be negative, which may cause confusing results
- Gas constant R changes with different units of pressure and volume
- Temperature is always in SI units of Kelvin, not Celsius, in gas equations
- Charles' Law works with Celsius, but the algebra is more complicated
Gas laws use Kelvin, not Celsius, because Kelvin is an absolute scale
Celsius, on the other hand, is an arbitrary scale where zero was chosen as the freezing point of water, which has nothing to do with gas laws. Using Celsius can lead to negative degrees, which may cause confusing results. For instance, if you were to plot the relationship between volume and temperature of a gas on a chart, the line would cross the Y-axis (temperature) at about -273 °C, not 0 °C. This can be avoided by using the Kelvin scale, where zero is absolute zero, making the maths simpler and neater.
Charles' Law, in particular, has to use Kelvin because using Celsius would result in negative numbers in some cases. Charles' Law states that under constant pressure, an ideal gas' volume is directly proportional to its absolute temperature. This was discovered by Jacques Charles around 1787 through an experiment where he filled five sites with the same volume with different gases. He then raised the temperature of the sites to 80 °C and noticed that they all increased in volume by the same amount.
Other absolute temperature scales such as Rankine would also work for gas laws, but arbitrary scales like Fahrenheit would not.
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Celsius is arbitrary and can be negative, which may cause confusing results
The degree Celsius is the unit of temperature on the Celsius temperature scale, which is one of two temperature scales used in the International System of Units (SI), the other being the Kelvin scale. The degree Celsius (symbol: °C) can refer to a specific point on the Celsius temperature scale or to a difference or range between two temperatures. The Celsius scale was first proposed by Swedish astronomer Anders Celsius in 1742.
Celsius is considered arbitrary because it is based on the freezing and boiling points of water, unlike the Kelvin scale, which is an absolute scale. On the Celsius scale, 0°C is the freezing point of water, and 100°C is the boiling point. This differs from the Kelvin scale, where 0 K is defined as absolute zero, the coldest temperature possible.
The arbitrary nature of the Celsius scale can lead to confusing results when negative temperatures are involved. While the Celsius scale can have negative values, indicating temperatures below the freezing point of water, these negative numbers are still above absolute zero. In contrast, the Kelvin scale can also have negative values, but a negative Kelvin temperature is actually hotter than any positive temperature, which can be counterintuitive and challenging to comprehend.
Additionally, the use of Celsius can be confusing when dealing with gas laws. Gas laws require temperature to be calculated on an absolute scale, which the Kelvin scale provides. Absolute zero, represented as 0 K, serves as a fixed reference point on the Kelvin scale, ensuring consistent and meaningful measurements in gas laws. In contrast, the Celsius scale lacks an absolute zero as its reference point, making it less suitable for precise calculations in gas laws.
Furthermore, the arbitrary nature of Celsius becomes evident when considering the historical context of its development. The original Celsius scale proposed by Anders Celsius was actually the reverse of the modern Celsius scale. In his scale, 0 represented the boiling point of water, while 100 represented the freezing point. It was later inverted by French physicist Jean-Pierre Christin in 1743, resulting in the Celsius scale commonly used today.
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Gas constant R changes with different units of pressure and volume
The gas constant, also known as the universal gas constant or molar constant, is denoted by the symbol R. It is a physical constant that appears in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation. The value of the gas constant R changes when dealing with different units of pressure and volume. This is because the gas constant is defined as the product of pressure and volume, and different units of pressure and volume will result in different numerical values for R.
The ideal gas law, which relates the state variables of pressure (P), volume (V), amount of substance (n), and temperature (T), is expressed as PV = nRT. The value of R in this equation depends on the units used for pressure and volume. For example, if the pressure is measured in atmospheres (atm) and the volume is measured in litres (L), the value of R will be different from when pressure is measured in pascals (Pa) and volume is measured in cubic metres (m^3).
The value of R at standard atmospheric pressure (1 atm) is approximately R = 8.3144598 J.mol-1.K-1. This value is known as the molar gas constant and is used when the pressure is in atm, the volume is in litres, and the temperature is in Kelvin. The US Standard Atmosphere, 1976 (USSA1976) defines a slightly different value for the gas constant R*, which is R* = 8.31432 J.K-1.mol-1. This value is used when the pressure is in N/m^2 (Pa), the volume is in m^3, and the temperature is in Kelvin.
It is important to note that the temperature is always in Kelvin when using the ideal gas equation. This is because Kelvin is an absolute temperature scale, whereas Celsius is arbitrary and can be negative, which may cause confusing results. Therefore, when dealing with different units of pressure and volume, the value of R will change accordingly, but the temperature unit remains constant in Kelvin.
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Temperature is always in SI units of Kelvin, not Celsius, in gas equations
The gas laws, including Charles's Law, the Ideal Gas Law, and Avogadro's Law, require temperature to be in Kelvin rather than Celsius. This is because Kelvin is an absolute scale, whereas Celsius is arbitrary. Absolute zero, or 0 Kelvin, is the coldest matter can be, whereas negative degrees are possible in Celsius, which can cause confusing results.
Temperature is always in SI units of Kelvin (K) in gas equations because Kelvin is an absolute scale. This means that 0 Kelvin is the point at which matter has no thermal energy and is absolute zero. On the Celsius scale, the zero point is arbitrary and does not represent the complete absence of thermal energy. Using an absolute scale for temperature is necessary for gas laws to work. For example, Charles's Law describes the direct relationship between the volume and temperature of a fixed amount of gas when pressure is held constant. If temperature is measured in an absolute scale, doubling the temperature will double the average kinetic energy of the molecules. However, if the temperature is doubled on the Celsius scale, the kinetic energy will not necessarily increase by the same amount.
The gas constant, R, in the Ideal Gas Law (PV=nRT) also depends on temperature being in Kelvin. The value of R changes depending on the units of pressure and volume, and the correct value of R must be used to get the correct answer. For example, if R is 0.082057 L atm mol-1K-1, the unit for pressure must be atm, the unit for volume must be litres, and the unit for temperature must be Kelvin.
While some sources state that Charles's Law does not work with Celsius, others argue that it does, with the algebra being only slightly more complicated. However, it is important to note that the standard condition of temperature and pressure (STP) is 1 atm (pressure) and 0°C, which must be converted to Kelvin when plugged into the Ideal Gas Equation or any other gas equations.
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Charles' Law works with Celsius, but the algebra is more complicated
Charles's Law, which states that if you double the temperature of a gas while keeping the pressure constant, its volume will also double, works with Celsius. However, the algebra becomes more complicated because of the arbitrary zero point of the Celsius scale.
The gas constant is always a constant, regardless of the temperature scale used. It is a fundamental constant relating the statistical properties of molecules to macroscopic phenomena like pressure and temperature. However, when using the Celsius scale, the zero point is arbitrary, and "zero" does not necessarily mean "no kinetic energy." This means that if you double the temperature as measured on an absolute scale, you are doubling the average kinetic energy of the molecules, but if you double the temperature on the Celsius scale, the kinetic energy does not necessarily increase by the same amount.
To use Charles's Law with Celsius temperatures, you can express it relative to T=0 absolute as V/T = k, where k is a constant. Then, if you convert T (K) to t (°C) as t = T-273, Charles's Law takes the form V/(t+273) = k. More generally, if you use a linear function of T, such as Y = mT + b, the equation becomes V/T = Vm/(Y-b) = k or V/(Y-b) = k/m, where k, b, and m are constants.
Using Celsius temperatures with Charles's Law requires determining two constants, k and b, which adds complexity to the algebra. Additionally, the Celsius scale allows for negative temperatures, which can cause confusing results. For these reasons, gas laws typically use the Kelvin scale, which is an absolute scale with a fixed zero point at absolute zero, the coldest matter can reach.
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Frequently asked questions
Kelvin is an absolute scale, whereas Celsius is arbitrary. The Kelvin scale uses absolute zero, the coldest matter can be, as its zero point. Gas laws require temperature to be calculated on an absolute scale. Celsius has negative values, which can cause confusing results.
No, Charles' Law does not work with Celsius. This is because the gas constant is not a constant when Celsius is used.
No, the Ideal Gas Law requires the use of Kelvin. The gas constant, R, will change when dealing with different units of pressure and volume.
