How Pressure Cookers Use Gas Laws To Work

The pressure cooker was invented in 1679 by French physicist Denis Papin, who used the laws of physics to create it. The key gas law that influences the pressure cooker is the Ideal Gas Law, also known as the Perfect Gas Law or the general gas equation. This law states that when pressure increases, the temperature increases. The Ideal Gas Law is represented by the formula PV = nRT, where P stands for pressure, V for volume, T for temperature, n for the amount of a given gas, and R for the ideal gas constant. In a pressure cooker, the volume and the amount of gas remain constant, so the formula can be simplified to P = T. This means that as pressure increases, so does temperature, and vice versa. The Ideal Gas Law explains why the boiling point of water increases in a pressure cooker, allowing food to cook faster at higher temperatures.

The Ideal Gas Law

This law is particularly relevant to pressure cookers, which were invented by the physicist Denis Papin in 1679. Papin's creation, known as the "steam digester," was the precursor to modern pressure cookers and steam engines. The key principle behind the pressure cooker is its ability to trap steam, leading to a rise in internal pressure. This increase in pressure, as explained by the Ideal Gas Law, results in a higher boiling point for water, typically exceeding 212°F (100°C).

\[ \dfrac{PV}{nRT}=1 \]

In this equation, the term \( \frac{pV}{nRT} \) is known as the compression factor and indicates the ideality of the gas. An ideal gas will always yield a value of 1 when used in this equation. Deviations from 1 suggest that the gas behaves more like a real gas rather than an ideal one.

It is important to note that the Ideal Gas Law serves as a foundation for other gas laws, including Boyle's Law, Charles's Law, and Avogadro's Law. These simpler gas laws can be derived from manipulations of the Ideal Gas Law. For example, Boyle's Law describes the inverse relationship between pressure and volume at a constant temperature and a fixed gas amount. Charles's Law, on the other hand, explains the direct relationship between volume and temperature (in Kelvin) when the pressure and gas amount remain constant.

Gay-Lussac's Law

Mathematically, this law can be expressed as:

P1/T1 = k, where P1 is the initial pressure and T1 is the initial temperature.

P2/T2 = k, where P2 is the final pressure and T2 is the final temperature.

Therefore, P1/T1 = P2/T2 = k.

This law implies that the ratio of the initial pressure and temperature is equal to the ratio of the final pressure and temperature for a gas of a fixed mass kept at a constant volume.

For example, in a pressure cooker, the steam generated as the contents are heated becomes trapped, leading to a rise in internal pressure. This increase in pressure drives the boiling point of water above its standard value of 212°F (100°C). The higher cooking temperature achieved in a sealed pressure cooker generally leads to faster cooking without burning the food.

Additionally, the sealed nature of the pressure cooker limits the evaporation of critical volatile flavour and aroma compounds, further enhancing the cooking process.

Boyle's Law

The law was formulated by Anglo-Irish physicist and chemist Robert Boyle in 1662, although French physicist Edme Mariotte discovered the same law independently in 1679.

Mathematically, Boyle's Law can be stated as:

P ∝ (1/V)

Or

P = k*(1/V) ⇒ PV = k

Where P is the pressure exerted by the gas, V is the volume occupied by it, and k is a constant for a particular temperature and amount of gas.

The law can be used to predict the increase in pressure exerted by a gas on the walls of its container when the volume of its container is decreased, as long as its quantity and absolute temperature remain unchanged. For example, when a filled balloon is squeezed, the volume of air inside the balloon decreases, and as a consequence of Boyle's Law, the pressure exerted by the air on the balloon increases, eventually popping it.

In the context of a pressure cooker, Boyle's Law influences the pressure cooker to a lesser extent, but not directly. This law allows liquids to heat higher than their normal boiling point because of the higher pressure in the pressure cooker.

Charle's Law

The pressure cooker was invented in 1679 by French physicist Denis Papin. Papin's design was based on the laws of physics, and the device operates according to the Ideal Gas Law. However, multiple gas laws influence the workings of a pressure cooker to some extent, including Charles' Law.

Charles' Law, also known as the Law of Volumes, is an experimental gas law that explains how gases tend to expand when heated. The law was formulated by French scientist Jacques Charles in the 1780s. It states that the volume and temperature of a fixed amount of gas are directly proportional to each other when pressure is kept constant. In other words, as temperature increases, volume increases, and as temperature decreases, volume decreases. This relationship can be expressed by the equation:

> V ∝ T

Where:

• V = volume
• T = absolute temperature

The equation can also be written as:

> V/T = k

Where:

K = a non-zero constant

For comparing a substance under two different sets of conditions, the law can be written as:

> \(\frac {V_i}{V_f} = \frac {T_i}{T_f}\)

Where:

• Vi = initial volume
• Vf = final volume
• Ti = initial temperature
• Tf = final temperature

This equation shows that as temperature increases, the volume of the gas also increases in proportion.

Charles' Law is applicable to ideal gases and real gases at high temperatures and low pressures. The relationship between volume and temperature is not linear at high pressures.

> A gas occupies 221 cm3 at a temperature of 0 °C and pressure of 760 mm Hg. Find its volume at 100 °C.

First, the pressure is constant, so it is not needed for the calculation. Convert the temperatures to Kelvin:

> V1 = 221 cm3

> T1 = 273 K (0 + 273)

> T2 = 373 K (100 + 273)

Now, plug the values into the equation and solve for V2:

> V1/T1 = V2/T2

> 221 cm3 / 273 K = V2 / 373 K

> V2 = (221 cm3)(373 K) / 273 K

> V2 = 302 cm3

So, the volume of the gas at 100 °C is 302 cm3.

Avogadro's Law

The fundamental principle behind a pressure cooker is the Ideal Gas Law, which states that pressure (P) times volume (V) equals the amount of substance (n) and the ideal gas constant (R) multiplied by temperature (T). This equation, PV = nRT, demonstrates the direct relationship between pressure and temperature, where an increase in one leads to an increase in the other.

One of the gas laws that influences the workings of a pressure cooker is Avogadro's Law. Avogadro's Law, also known as Avogadro's hypothesis or principle, is an experimental gas law that relates the volume of a gas to the amount of substance of gas present. Formulated by Amedeo Avogadro in 1811 and published in 1811 or 1812, the law states that "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules." This means that under the same conditions of temperature and pressure, different gases will have the same number of molecules if they occupy the same volume.

Mathematically, Avogadro's Law can be expressed as:

V ∝ n

Or

V/n = k

Where V is the volume of the gas, n is the amount of substance of the gas (measured in moles), and k is a constant for a given temperature and pressure. This law is a specific case of the Ideal Gas Law, which can be derived from it.

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