This all-in-one online Gay-Lussac’s Law Calculator performs calculations using the Gay-Lussac’s law formula that relates the initial and final pressure and temperature values of an ideal gas at the same constant volume. You can enter the values of any three parameters in the fields of the calculator and find the missing parameter.
P1 / T1 = P2 / T2
Gay-Lussac’s Law
Gay-Lussac’s Law is an experimental gas law that relates the pressure and temperature of a fixed mass of a gas that is close to an ideal gas when its volume remains constant. The law, also known as the law of pressure–temperature, was named after scientist Joseph Louis Gay-Lussac, who first discovered it.
The law in modern formulation states that when the volume on a sample of gas is held constant, the Kelvin temperature and the pressure will be in direct proportion. This relationship of direct proportion can be written as the following Gay-Lussac’s law formula:
$$P = k \cdot T,$$
where
• \(P \ \) is the pressure of the gas,
• \(T \ \) is the temperature of the gas (measured in Kelvins),
• \(k \ \) is a non-zero constant.
The Gay-Lussac’s law is often expressed in the following form:
$$\frac{P_1}{T_1} = \frac{P_2}{T_2},$$
where
• \(P_1 \ \) is the initial pressure,
• \(T_1 \ \) is the initial temperature (in Kelvins),
• \(P_2 \ \) is the final pressure,
• \(T_2 \ \) is the final temperature (in Kelvins).
It should be emphasized that the above formulas use temperature measured in Kelvin. Recall that the Kelvin is the SI unit for temperature and is sometimes referred to as absolute temperature. If you want to use other temperature units, you must use the following conversion formulas:
$$Celsius = Kelvin \ – \ 273.15,$$
$$Fahrenheit = \frac{9}{5} \cdot Celsius + 32.$$
These conversions are done automatically when you use our Gay-Lussac’s Law calculator and select the units you need.
When using the Gay-Lussac’s law, remember that it only applies to gases that are close to an ideal gas. An ideal gas consists of particles of negligibly small size that do not interact with each other. The ideal gas model makes it easy to understand the physical meaning of Gay-Lussac’s law.
Indeed, an increase in the temperature of a gas causes individual gas molecules to move faster. The faster the molecules move, the more often and with greater force they collide with the walls of the gas container. More frequent and forceful collisions result in higher pressure, provided the volume of the container remains constant. The thermodynamic process in which the volume of the system is maintained constant is called isochoric.
The reverse process occurs when the gas temperature decreases. As can be seen from the above formula, when the temperature decreases to zero, the pressure of the gas also tends to zero. The temperature of 0 K = -273.15 ºC is called absolute zero. According to classical physics, at this temperature all motion ceases, therefore the pressure vanishes.
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