2.3 Temperature, Pressure, and Composition Scales

Temperature scales are essential in chemical engineering, allowing us to measure and compare heat levels. From Celsius to Kelvin, each scale serves a unique purpose, with conversion formulas bridging the gaps between them.

Pressure and composition scales are equally crucial, helping engineers quantify forces and mixture components. Understanding these scales and how to convert between them is fundamental for solving complex chemical process problems.

Temperature Scales

Temperature scales and conversions

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• Celsius (°C) measures water's freezing (0°C) and boiling (100°C) points used globally for everyday measurements
• Kelvin (K) absolute temperature scale starts at 0 K (absolute zero) employed in scientific calculations
• Fahrenheit (°F) prevalent in the United States defines water's freezing at 32°F and boiling at 212°F
• Rankine (°R) absolute temperature scale relates to Fahrenheit with 0°R at absolute zero
• Conversion formulas enable switching between scales:
  • $K = °C + 273.15$
  • $°F = (°C × 9/5) + 32$
  • $°R = K × 1.8$
  • $°R = °F + 459.67$

Pressure and Composition Scales

Pressure scales and conversions

• Absolute pressure measured from perfect vacuum (zero pressure) always positive used in thermodynamics
• Gauge pressure measured relative to atmospheric pressure can be positive or negative common in industry
• Vacuum pressure represents negative gauge pressure below atmospheric pressure
• Atmospheric pressure standard value: 1 atm = 101.325 kPa = 14.7 psi
• Conversion formulas:
  • Absolute pressure = Gauge pressure + Atmospheric pressure
  • Vacuum pressure = Atmospheric pressure - Absolute pressure

Composition representations in chemistry

• Composition quantifies relative amounts of components in mixtures
• Mass fraction ratio of component mass to total mixture mass (sum = 1)
• Mole fraction ratio of component moles to total mixture moles (sum = 1)
• Volume fraction ratio of component volume to total mixture volume (ideal gases)
• Concentration measures mass of solute per unit volume of solution (g/L, mol/L)

Composition calculations and conversions

• Mass fraction to mole fraction:
  1. Divide mass fraction by molecular weight
  2. Normalize results to ensure sum equals 1
• Mole fraction to mass fraction:
  1. Multiply mole fraction by molecular weight
  2. Normalize results to ensure sum equals 1
• Volume fraction equals mole fraction for ideal gas mixtures (Amagat's law)
• Concentration calculations include molarity (moles solute/liter solution) and molality (moles solute/kg solvent)
• Density and specific gravity relate mass and volume fractions

Applications of temperature, pressure, and composition

• Material balances require consistent units for temperature and pressure with appropriate composition conversions
• Vapor-liquid equilibrium calculations use absolute pressure and temperature scales considering partial pressures and mole fractions
• Gas law applications (Ideal gas law: $PV = nRT$) employ absolute temperature and pressure scales
• Heat transfer problems apply temperature conversion formulas and consider temperature-dependent properties
• Reaction kinetics utilize appropriate composition scales (concentrations) and account for temperature effects on reaction rates