Pressure & Gas Laws – Quick Review Notes

Pressure Basics

• Definition: force applied per unit area
  P = \frac{F}{A}
• SI unit: \text{Pa (N/m}^2); common units: \text{kPa, bar, atm, psi, mmHg (cmHg), mH_2O, kg/cm}^2
• Conversion essentials (see full table):
  • 1\,\text{bar}=100\,\text{kPa}=14.5\,\text{psi}=75.006\,\text{cmHg}

Static Pressure (Liquids)

• Caused by weight of fluid column above a point
• Formula: P = \rho g h
  • \rho density (kg/m^3)
  • g gravity (≈ 9.81\,\text{N/kg})
  • h depth (m)
• Increases with: depth, fluid density, gravitational acceleration
• Acts equally in all directions; normal to surfaces

Hydraulic Pressure & Pascal’s Law

• Liquids: incompressible; transmit pressure equally in closed system
• Pascal’s Law: external pressure on confined liquid is transmitted undiminished throughout
• Relation between pistons:
  P1=P2 \;\Rightarrow\; \frac{F1}{A1}=\frac{F2}{A2}
  F2 = F1\frac{A2}{A1} (force amplification)
• Applications: car brakes, hydraulic jacks, forklift trucks, lifts

Atmospheric & Gas Pressure

• Atmospheric pressure: weight of air column above surface (~101\,\text{kPa} at sea level)
• Decreases with altitude; depends on air density & temperature
• Measuring devices:
  • Atmospheric: mercury barometer, aneroid barometer
  • Gas: manometer, pressure gauge
• Manometer relations:
  PG = PA + \Delta P (open)
  PG = \Delta P (closed/vacuum limb) \Delta P = h(\rho g); convert height of Hg/H2O to pressure using table

Gas Laws (fixed mass of gas)

• Boyle’s Law (T constant): P1 V1 = P2 V2 (pressure ↑ ⇒ volume ↓)
• Charles’s Law (P constant): \frac{V1}{T1}=\frac{V2}{T2} (temperature in K)
• Gay-Lussac’s Law (V constant): \frac{P1}{T1}=\frac{P2}{T2}
• Combined Gas Law: \frac{P1 V1}{T1}=\frac{P2 V2}{T2} (no variable held constant)
• Always convert °C to K: T(K)=T(°C)+273

Problem-Solving Reminders

• Keep units consistent; convert pressure units before substituting
• Use area in \text{m}^2, force in N for P=\frac{F}{A}
• For liquid columns, height in meters unless conversion factor used
• Show all steps & check answer magnitude against typical values