2.2 P-v-T behavior of pure substances

Pressure, volume, and temperature are the building blocks of thermodynamics. These properties help us understand how substances behave under different conditions. Knowing how they interact is key to grasping the bigger picture of pure substances.

Constant property processes like isothermal, isobaric, and isochoric give us a way to analyze substance behavior. By keeping one property constant, we can see how the others change. This helps us predict and control substance behavior in real-world applications.

Thermodynamic Properties

Pressure, Volume, and Temperature

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• Pressure ($P$) represents the force per unit area exerted by a fluid
  • Measured in units such as pascals (Pa), bars, or pounds per square inch (psi)
  • Atmospheric pressure at sea level is approximately 101,325 Pa or 1 atm
• Specific volume ($v$) is the volume occupied by a unit mass of a substance
  • Reciprocal of density ($\rho$) and is expressed as $v = 1/\rho$
  • Commonly measured in units such as cubic meters per kilogram (m³/kg) or cubic feet per pound (ft³/lb)
• Temperature ($T$) is a measure of the average kinetic energy of the particles in a substance
  • Expressed in units of Kelvin (K) or degrees Celsius (°C) for SI units and Rankine (°R) or Fahrenheit (°F) for English units
  • Absolute zero is the lowest possible temperature, corresponding to 0 K or -273.15 °C

Constant Property Processes

Isothermal, Isobaric, and Isochoric Processes

• Isotherms are processes that occur at constant temperature
  • On a P-v diagram, isotherms appear as hyperbolic curves for an ideal gas
  • For an ideal gas undergoing an isothermal process, the product of pressure and volume remains constant ($PV = constant$)
• Isobars are processes that occur at constant pressure
  • On a P-v diagram, isobars appear as horizontal lines
  • During an isobaric process, the volume of a substance changes while the pressure remains constant
• Isochores are processes that occur at constant volume
  • On a P-v diagram, isochores appear as vertical lines
  • During an isochoric process, the pressure of a substance changes while the volume remains constant

Material Behavior

Compressibility and Thermal Expansion

• Compressibility is a measure of a substance's ability to change its volume in response to a change in pressure
  • Isothermal compressibility ($\beta_T$) is defined as $\beta_T = -\frac{1}{v} \left(\frac{\partial v}{\partial P}\right)_T$
  • Substances with high compressibility (gases) experience significant volume changes with pressure, while those with low compressibility (liquids and solids) experience minimal volume changes
• Thermal expansion is the tendency of a substance to change its volume in response to a change in temperature
  • Volumetric thermal expansion coefficient ($\alpha_v$) is defined as $\alpha_v = \frac{1}{v} \left(\frac{\partial v}{\partial T}\right)_P$
  • Most substances expand when heated and contract when cooled, with gases exhibiting the highest thermal expansion, followed by liquids and solids
  • Water is an exception, as it expands when cooled from 4 °C to 0 °C due to its unique molecular structure