Every day, often without realizing it, we experience the laws of gas thermodynamics. When you inflate a bicycle tire or a pressure cooker valve releases a jet of steam, the behavior of the gas follows a fundamental relationship: the ideal gas law. This law, developed by several physicists, simply relates three essential physical quantities: pressure, the volume occupied by the gas, and the absolute temperature.
An ideal gas is a theoretical model where molecules are treated as point masses with no volume or interactions, except for perfectly elastic collisions. Their random motion and thermal agitation directly relate pressure, volume, and temperature, leading to a simple and universal state equation: \(PV = nRT\).
This model is called "ideal" because it accurately describes the behavior of gases at low pressure and high temperature, where real interactions become negligible.
All physical gases are real gases, and the ideal gas does not exist as a substance. It only exists as a theoretical model. But this model is not arbitrary fiction: it is a physically well-defined limiting approximation.
All existing gases deviate from the ideal model because their molecules have a finite volume and exert interactions on each other. At high pressure, the volume occupied by molecules is no longer negligible: the gas becomes less compressible than predicted by the ideal model. At low temperature, intermolecular attractive forces reduce the pressure exerted on the walls.
The ideal gas law is one of the most fundamental in thermodynamics. It relates four important variables describing a gas: pressure (\(P\)), volume (\(V\)), temperature (\(T\)), and the amount of gas (\(n\)).
N.B.:
Temperature must always be expressed in kelvins in the equation. Using degrees Celsius will systematically produce incorrect results.
The ideal gas equation is a valid approximation at moderate temperature and pressure, where real gases behave almost like ideal gases. The equation tells us that, for a given amount of gas (\(n\)) and constant temperature (\(T\)), pressure and volume are inversely related. This means that if you increase the volume, the pressure decreases, and vice versa, provided the temperature and amount of gas remain constant.
When you use a bicycle pump, the pressure of the gas inside the pump increases as you compress the air. The observed thermal effect—that the pump heats up—is a direct consequence of the ideal gas law (\(PV = nRT\)).
When you operate the pump, you exert a force to reduce the volume of the gas inside the pump. According to the ideal gas law, if the volume (\(V\)) decreases while keeping the amount of gas (\(n\)) constant, the pressure (\(P\)) must increase. When a gas is compressed, it releases energy in the form of heat.
The phenomenon where the refrigerator door becomes difficult to open after leaving it open for a while, especially in summer, can be explained by the ideal gas law (\(PV = nRT\)).
When you leave the refrigerator door open for some time, the air inside mixes with the warm ambient air. This warm air increases the temperature inside the refrigerator. When you close the door, the gas inside begins to cool again, and its pressure decreases. As a result, the outside air exerts greater pressure on the closed door, making it harder to open.
When you turn a hot jam jar upside down after sealing it, the air inside the jar cools rapidly. As it cools, the air inside the jar contracts.
According to the ideal gas law (\(PV = nRT\)), if the temperature decreases at constant volume, the pressure inside the jar also decreases. This happens because the gas loses kinetic energy, and the air molecules occupy less space. This reduction in temperature and pressure creates a partial vacuum inside the jar relative to the external atmospheric pressure.
Due to this partial vacuum inside the jar, you may hear a slight "pop" when the jar is turned over and the lid deforms slightly inward. This occurs because the external pressure is greater than the pressure inside the jar. This phenomenon is not a perfect vacuum but a very low pressure that creates a hermetic seal.
The ideal gas equation (\(PV = nRT\)) shows that pressure is directly related to temperature and volume in a gas. In the case of boiling water, water vapor escapes from the surface of the water. When the water vapor pressure equals atmospheric pressure, the boiling point is reached, and evaporation maintains this boiling temperature.
At higher altitudes, atmospheric pressure decreases compared to sea level. This affects the boiling point of water, which is closely related to ambient pressure. At high altitudes, where atmospheric pressure is lower, water boils at a lower temperature. For example, at 2000 meters above sea level, water boils at about 93°C, and at 4000 meters, at 86°C.
Cooking pasta depends on the temperature at which the water remains during boiling. Since water boils at a lower temperature at altitude, the temperature at which the pasta cooks is also lower. Because water cannot reach the higher temperatures found at sea level (100°C), cooking pasta at altitude will be slower.
The operation of a pressure cooker perfectly illustrates the application of the ideal gas law (\(PV = nRT\)).
A pressure cooker works by increasing the pressure inside the pot. As the water heats up, its temperature rises, and the water vapor generates increasing pressure inside the cooker. When the pressure increases (with the volume remaining constant because the lid is closed), the boiling point of the water also increases. In other words, in a pressure cooker, water can reach a temperature higher than 100°C before it starts to boil. For example, at a pressure of about 2 bars (twice atmospheric pressure), water boils at about 120°C.
In the ideal gas law (\(PV = nRT\)), the three variables \(P\), \(V\), and \(T\) are interdependent: changing one necessarily affects at least one other. You cannot increase the pressure in a fixed volume without the temperature rising. Conversely, you cannot reduce the volume at constant temperature without the pressure increasing. Similarly, you cannot cool a confined gas without the pressure dropping.
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