How to Convert Between Different Units of Pressure in Physics?
Pressure is a fundamental concept in physics and chemistry, representing the amount of force distributed over a unit area. It describes how forces are transmitted through solids, liquids, and gases, affecting systems from atmospheric air to hydraulic machines and biological tissues. A clear understanding of pressure and its units is essential for mastering various scientific topics and problem-solving techniques.
Definition and Formula of Pressure
Pressure is defined as the force exerted perpendicularly on a unit area of a surface. Mathematically, it is expressed as:
Where P is pressure, F is the magnitude of the force (in newtons), and A is the area (in square meters) over which the force is applied.
System of Units for Pressure
The International System of Units (SI) uses the pascal (Pa) as the standard unit of pressure. One pascal is equal to one newton of force applied over one square meter of area:
Since the pascal is a small unit, multiples such as the kilopascal (kPa, 1,000 Pa) and megapascal (MPa, 1,000,000 Pa) are commonly used. In addition, practical and historical units, such as atmosphere (atm), bar, millimeter of mercury (mm Hg or Torr), and pounds per square inch (psi), are encountered in various applications.
| Unit | Symbol | System | Relation to Pascal |
|---|---|---|---|
| Pascal | Pa | SI | 1 Pa = 1 N/m² |
| Bar | bar | Practical/Metric | 1 bar = 100,000 Pa |
| Atmosphere | atm | Practical | 1 atm = 101,325 Pa |
| Millimeter of Mercury (Torr) | mm Hg (Torr) | Practical | 1 mm Hg = 133.322 Pa |
| Pounds per Square Inch | psi | Imperial | 1 psi ≈ 6,894.76 Pa |
| Barye | Ba | CGS | 1 Ba = 0.1 Pa |
Physical Meaning and Examples
Pressure is a scalar quantity that acts equally in all directions in a fluid at rest. For example, the pressure experienced on the soles of your shoes while standing, the pressure in automobile tires, or atmospheric pressure pressing on all objects at sea level are all manifestations of this concept.
| Scenario | Typical Pressure | Unit |
|---|---|---|
| Atmospheric pressure at sea level | 101,325 | Pa (1 atm) |
| Car tire pressure | 2.0 × 10⁵ | Pa (29 psi) |
| Hydraulic jack | 1 × 10⁷ | Pa (100 bar) |
| Deep ocean (Marianas Trench) | 1 × 10⁸ | Pa (1000 bar) |
Common Formulas Involving Pressure
| Formula | Context |
|---|---|
| P = F / A | Basic definition: force on area |
| P = hρg | Hydrostatic pressure at depth h (ρ: density, g: gravity) |
| P = nRT / V | Ideal gas law (n: moles; R: gas constant; T: temperature; V: volume) |
Pressure Unit Conversion Table
| From | To | Multiply By |
|---|---|---|
| atm | Pa | 101325 |
| bar | Pa | 100000 |
| Torr (mm Hg) | Pa | 133.322 |
| psi | Pa | 6894.76 |
Typical Steps for Solving Pressure Problems
- Write down what's given: force, area, depth, etc.
- Convert all values to SI units when using SI formulas.
- Use the appropriate formula (e.g., P = F/A or P = hρg).
- Plug in values and solve for pressure or the unknown.
- If needed, convert your answer to the required pressure unit using the table above.
Example Problem and Solution
Example: If a force of 40 N is applied uniformly over an area of 2 m², what is the resulting pressure in pascals?
The resulting pressure is 20 pascals (Pa).
Key Points and Summary
- The SI unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m².
- Common practical units are atm, bar, mm Hg (Torr), and psi — always double-check units in calculations.
- Pressure can be measured directly, or as gauge or absolute pressure, depending on the reference point.
- Consistent unit use throughout calculations is critical for correct answers in physics and chemistry.
Further Learning and Vedantu Resources
- Pressure: Concepts and Numericals
- Unit of Pressure
- Atmospheric Pressure
- Hydrostatic and Fluid Pressure
- Pressure in Drops, Bubbles, and Capillary Rise
Mastering the concept of units of pressure will help you excel in mechanics, thermodynamics, and real-world data analysis. Practice regularly using the problem-solving steps and always use the correct units.
FAQs on Unit of Pressure in Physics: SI and Other Standard Units Explained
1. What is the SI unit of pressure?
The SI unit of pressure is the Pascal (Pa). One Pascal is defined as 1 Newton per square metre (1 N/m²), meaning a force of 1 Newton applied evenly across an area of 1 square metre. This is the standard unit used in most scientific and engineering practices for measuring pressure.
2. How is pressure defined in Physics?
Pressure is defined as the force applied per unit area. It quantifies how much force is exerted on a surface, calculated using the formula:
- Pressure (P) = Force (F) / Area (A)
- The SI unit is Pascal (Pa), where 1 Pa = 1 N/m².
- Pressure is a scalar quantity used in physics, chemistry, and engineering.
3. What are the practical units of pressure commonly used?
Apart from Pascal (Pa), several practical units of pressure are used:
- Atmosphere (atm): 1 atm = 101,325 Pa
- Bar: 1 bar = 100,000 Pa
- Millimeter of mercury (mm Hg) or Torr: 1 mm Hg = 133.322 Pa
- Pounds per square inch (psi): Used mainly in the US
These units are useful in various contexts such as atmospheric science, chemistry, and engineering.
4. What is the CGS unit of pressure and its relationship to SI?
The CGS unit of pressure is the barye (Ba).
- 1 barye (Ba) = 1 dyne/cm²
- To convert: 1 Pa = 10 Ba (i.e., 1 Ba = 0.1 Pa).
- The CGS system is less commonly used today, but conversions may be needed for competitive exams or older literature.
5. How do you convert atm and bar to pascal (Pa)?
Conversions between pressure units are standard:
- 1 atmosphere (atm) = 101,325 Pa
- 1 bar = 100,000 Pa
- 1 mm Hg (Torr) = 133.322 Pa
Tip: Always use the correct conversion factor for numerical problems.
6. Which unit is often used for pressure in the ideal gas law (PV=nRT)?
In the ideal gas law (PV = nRT), the standard unit for pressure is the Pascal (Pa) in SI. Sometimes, atmosphere (atm) is also used, especially in chemistry, with R (the gas constant) adjusted accordingly:
- If P is in Pa, use R = 8.314 J/(mol·K)
- If P is in atm, use R = 0.0821 L·atm/(mol·K)
7. What is the formula and dimensional formula of pressure?
The formula for pressure:
- P = F / A (Pressure = Force / Area)
- SI Unit: Pascal (Pa) = N/m²
- Dimensional formula: [M L-1 T-2]
This dimension shows that pressure is derived from mass, length, and time units.
8. Can you list the most important pressure unit conversions for exams?
Key pressure conversions:
- 1 atm = 101,325 Pa
- 1 bar = 100,000 Pa
- 1 mm Hg = 133.322 Pa
- 1 Pa = 10 Ba (barye)
These conversions are frequently tested in board and entrance exam numericals.
9. What is the difference between absolute and gauge pressure?
Absolute pressure is measured relative to a perfect vacuum, while gauge pressure is measured relative to atmospheric pressure.
- Gauge Pressure = Absolute Pressure – Atmospheric Pressure
- Most pressure-measuring devices (like tire gauges) show gauge pressure.
- Understanding this difference helps prevent calculation mistakes in Physics and Chemistry problems.
10. Why are pressure units important in Physics and Chemistry?
Pressure units are fundamental because they are used across multiple chapters in Physics and Chemistry, including mechanics, thermodynamics, and gas laws.
- Correct unit usage ensures accurate calculations.
- Many numerical errors occur from wrong unit conversions.
- Board and entrance exams test pressure concepts in both subjects.
11. What are the main applications of pressure in daily life?
Pressure concepts are applied in many real-world scenarios:
- Atmospheric pressure measurement (weather forecasting)
- Blood pressure monitoring in medicine
- Sports equipment (football, tires) inflation
- Hydraulics and fluid mechanics
- Industrial processes involving gases and liquids
12. How to avoid mistakes in pressure unit numericals during exams?
To avoid mistakes in pressure numericals:
- Always check and convert all units to the SI system before calculation.
- Write units with every value.
- Use standard conversion factors.
- Review formulas and dimensions.
This practice minimizes calculation errors and boosts exam confidence.
