Measurement of Pressure
Barometers, Manometers, and Interconverting Units.
Gas laws mathematically relate Pressure, Volume, Temperature, and Moles. One of the most common sources of error in numericals is using mismatched units. Let's master the concept of pressure, how it's measured, and how to flawlessly convert its units.
1. What is Gas Pressure?
Macroscopically, pressure ($P$) is defined as the force ($F$) exerted perpendicularly on a unit area ($A$) of a surface.
Microscopically, gas pressure arises from the continuous, random collisions of gas molecules against the walls of their container. Each collision exerts a tiny force; the sum of all these forces over a given area is the macroscopic pressure.
2. Devices for Measuring Pressure
A. The Barometer (Measures Atmospheric Pressure)
Invented by Torricelli, a barometer measures the pressure of the open atmosphere. It consists of a glass tube filled with mercury ($Hg$) inverted in a dish of mercury. The atmospheric pressure pushes down on the dish, forcing mercury up the tube.
- At sea level, the atmosphere supports a mercury column of 760 mm (or 76 cm).
- Pressure formula: $P = h \times \rho \times g$ (where $h$ is height, $\rho$ is density, and $g$ is gravity).
- Mercury is used because its high density allows for a reasonably short tube ($\sim$1 meter) instead of a massive one (water would require a 10.3-meter tube!).
B. The Manometer (Measures Trapped Gas Pressure)
A manometer is used to measure the pressure of a gas trapped inside a closed container. It typically consists of a U-shaped tube containing mercury.
- Closed-tube Manometer: The space above the mercury in the outer arm is a vacuum. The pressure of the gas directly equals the height difference ($\Delta h$).
- Open-tube Manometer: The outer arm is open to the atmosphere. The pressure of the gas is $P_{gas} = P_{atm} \pm \Delta h$.
3. Units of Pressure
Because pressure has been studied for centuries across different fields, multiple units are used. You must be able to convert between them instantly.
| Unit Name | Symbol | Definition / Note |
|---|---|---|
| Atmosphere | $atm$ | Standard pressure at sea level. Commonly used in Ideal Gas Equation. |
| Pascal | $Pa$ | The SI Unit. $1 \text{ Pa} = 1 \text{ Newton/m}^2$ ($N \cdot m^{-2}$). Often used as kilopascal ($kPa$). |
| Millimeters of Mercury | $mmHg$ | Based on the barometer reading. Also called torr (after Torricelli). |
| Bar | $bar$ | Widely used in meteorology and standard state thermodynamics. Very close to $1 \text{ atm}$. |
4. The Interconversion Guide
Memorize this exact equivalence block. It is the key to solving numericals in the Gaseous State and Thermodynamics.
$1 \text{ atm}$ is slightly larger than $1 \text{ bar}$.
Knowledge Check
Test your ability to convert pressure units
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