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Gay-Lussac Law
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Gay-Lussac's law states that the ratio of the pressure ($p$) to the absolute temperature ($T$) remains constant while the volume and the number of moles are kept constant.
This implies that the pressure ($p$) varies proportionally to the absolute temperature ($T$).
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Mechanisms
Iframe
The Gay-Lussac law states that the pressure of a gas is directly proportional to its temperature when the volume is held constant. This means that as the temperature of a gas increases, its pressure also increases, provided the volume does not change. Conversely, if the temperature decreases, the pressure decreases. This relationship is crucial for understanding the behavior of gases in closed containers, where an increase in temperature leads to an increase in pressure, and a decrease in temperature leads to a decrease in pressure.
Mechanisms
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Pressure and temperature variation
Concept
The pressure ($p$) is generated when gas particles collide with the surface of the gas container. Since the absolute temperature ($T$) is constant, the energy of the particles does not vary, and the collisions of these particles with the surfaces of the gas container will not vary in the transferred impulse. The pressure ($p$) is generated when gas particles collide with the surface of the gas container. Each collision transmits a momentum equal to twice the particle mass ($m$) times the average speed of a particle ($\bar{v}$). Additionally, it's important to consider the flow of particles towards the surface, which depends on the particle concentration ($c_n$) but also on the average speed of a particle ($\bar{v}$) with which they move. Therefore,
$p \propto c_n v \cdot m v = c_n m v^2$
The particle flow and momentum transmission are represented in the following graph:
Furthermore, the particle mass ($m$) times the average speed of a particle ($\bar{v}$) squared is proportional to the energy of a molecule ($E$), which in turn is proportional to the absolute temperature ($T$):
$p \propto c_n mv^2 \propto E \propto T$
In this case, when the volume ($V$) and the number of particles ($N$) are constant, so is the particle concentration ($c_n$).
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Temperature vs. pressure relationship
Description
In a gas, when the volume ($V$) and the number of particles ($N$) are held constant, it is observed that the pressure ($p$) and the absolute temperature ($T$) vary proportionally. When the absolute temperature ($T$) decreases, the pressure ($p$) also decreases, and vice versa,
$p \propto T$
as shown in the following graph:
Gay-Lussac's law [1] states that when the volume ($V$) and the number of particles ($N$) are held constant, the pressure ($p$) and the absolute temperature ($T$) are directly proportional.
This is expressed with the gay Lussac's law constant ($C_g$) as follows:
| $\displaystyle\frac{ p }{ T } = C_g$ |
[1] "Memoir on the Combination of Gaseous Substances with Each Other," Joseph Louis Gay-Lussac, Annales scientifiques de l'É.N.S. 3rd series, tome 3 (1886)
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Joseph Louis Gay Lussac
Description
Joseph Louis Gay-Lussac was a French chemist and physicist who lived from 1778 to 1850. He made significant contributions to the fields of chemistry and gas laws. Gay-Lussac conducted numerous experiments and investigations, particularly on the properties of gases, and formulated several important laws and principles. One of his notable achievements was the discovery of the law of combining volumes, known as Gay-Lussac's law. He also contributed to the study of electrolysis, the measurement of temperature, and the understanding of chemical reactions. Gay-Lussac's work greatly influenced the development of chemistry and laid the foundation for modern chemical theories.
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Change of state of an ideal gas according to the Gay Lussac Law
Concept
The Gay-Lussac's law states that when volume ($V$) and the number of particles ($N$) are held constant, the ratio of the pressure ($p$) to the absolute temperature ($T$) equals the gay Lussac's law constant ($C_g$):
| $\displaystyle\frac{ p }{ T } = C_g$ |
This implies that if a gas transitions from an initial state (the pressure in initial state ($p_i$) and the temperature in initial state ($T_i$)) to a final state (the pressure in final state ($p_f$) and the temperature in final state ($T_f$)) while keeping the pressure ($p$) and the number of particles ($N$) constant, Gay-Lussac's law must always hold true:
$\displaystyle\frac{p_i}{T_i}=C_g=\displaystyle\frac{p_f}{T_f}$
Thus, it follows:
| $\displaystyle\frac{ p_i }{ T_i }=\displaystyle\frac{ p_f }{ T_f }$ |
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Model
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Equations
$\displaystyle\frac{ p_i }{ T_i } = C_g$
p / T = g
$\displaystyle\frac{ p_f }{ T_f } = C_g$
p / T = g
$\displaystyle\frac{ p_i }{ T_i }=\displaystyle\frac{ p_f }{ T_f }$
p_i / T_i = p_f / T_f
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Gay Lussac Law (1)
Equation
Gay-Lussac's law [1] states that when the volume ($V$) and the number of particles ($N$) are held constant, the pressure ($p$) and the absolute temperature ($T$) are directly proportional.
This is expressed with the gay Lussac's law constant ($C_g$) as follows:
| $\displaystyle\frac{ p_i }{ T_i } = C_g$ |
| $\displaystyle\frac{ p }{ T } = C_g$ |
[1] "Memoir on the Combination of Gaseous Substances with Each Other," Joseph Louis Gay-Lussac, Annales scientifiques de l'É.N.S. 3rd series, tome 3 (1886)
ID:(581, 1)
Gay Lussac Law (2)
Equation
Gay-Lussac's law [1] states that when the volume ($V$) and the number of particles ($N$) are held constant, the pressure ($p$) and the absolute temperature ($T$) are directly proportional.
This is expressed with the gay Lussac's law constant ($C_g$) as follows:
| $\displaystyle\frac{ p_f }{ T_f } = C_g$ |
| $\displaystyle\frac{ p }{ T } = C_g$ |
[1] "Memoir on the Combination of Gaseous Substances with Each Other," Joseph Louis Gay-Lussac, Annales scientifiques de l'É.N.S. 3rd series, tome 3 (1886)
ID:(581, 2)
Change of state of an ideal gas according to the Gay Lussac Law
Equation
If a gas transitions from an initial state (i) to a final state (f) with the pressure ($p$) and the number of particles ($N$) held constant, it follows that for the pressure in initial state ($p_i$), the pressure in final state ($p_f$), the temperature in initial state ($T_i$), and the temperature in final state ($T_f$):
| $\displaystyle\frac{ p_i }{ T_i }=\displaystyle\frac{ p_f }{ T_f }$ |
The Gay-Lussac's law states that when volume ($V$) and the number of particles ($N$) are held constant, the ratio of the pressure ($p$) to the absolute temperature ($T$) equals the gay Lussac's law constant ($C_g$):
| $\displaystyle\frac{ p }{ T } = C_g$ |
This implies that if a gas transitions from an initial state (the pressure in initial state ($p_i$) and the temperature in initial state ($T_i$)) to a final state (the pressure in final state ($p_f$) and the temperature in final state ($T_f$)) while keeping the pressure ($p$) and the number of particles ($N$) constant, Gay-Lussac's law must always hold true:
$\displaystyle\frac{p_i}{T_i}=C_g=\displaystyle\frac{p_f}{T_f}$
Thus, it follows:
| $\displaystyle\frac{ p_i }{ T_i }=\displaystyle\frac{ p_f }{ T_f }$ |
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