Thermodynamic Properties Of Pure Substances Table

Thermodynamic properties of pure substances are crucial for engineers and scientists in designing and analyzing various thermal systems. These properties, such as temperature, pressure, volume, enthalpy, entropy, and internal energy, help to understand the behavior of substances under different conditions. Using thermodynamic tables, one can easily find the necessary property values for calculations, making the design and analysis process more efficient and accurate.

Introduction to Thermodynamic Properties

In thermodynamics, a pure substance is defined as a substance that has a fixed chemical composition throughout. Examples include water, nitrogen, oxygen, and helium. These substances can exist in different phases: solid, liquid, and gas (vapor). Understanding the thermodynamic properties of these pure substances is essential in many engineering applications, such as power generation, refrigeration, and chemical processes.

Key Thermodynamic Properties

1. Temperature (T): A measure of the average kinetic energy of the particles in a substance. Commonly measured in Celsius (°C) or Kelvin (K).
2. Pressure (P): The force exerted per unit area. Commonly measured in Pascals (Pa), bar, or atmospheres (atm).
3. Volume (V): The amount of space a substance occupies. Specific volume (v) is the volume per unit mass (m³/kg).
4. Internal Energy (U): The total energy contained within a substance, including kinetic and potential energy of its molecules. Specific internal energy (u) is the internal energy per unit mass (kJ/kg).
5. Enthalpy (H): A thermodynamic property that combines internal energy, pressure, and volume. Defined as H = U + PV. Specific enthalpy (h) is the enthalpy per unit mass (kJ/kg).
6. Entropy (S): A measure of the disorder or randomness of a system. Specific entropy (s) is the entropy per unit mass (kJ/kg·K).

Importance of Thermodynamic Tables

Thermodynamic tables provide a compilation of property values for various substances at different temperatures and pressures. These tables are invaluable because:

• They allow engineers to quickly look up property values without having to perform complex calculations.
• They provide accurate data that has been experimentally determined and verified.
• They help in understanding the behavior of substances under various conditions.

Understanding Thermodynamic Tables

Thermodynamic tables are organized to provide specific property values for a substance at different states. The most common tables are for water (steam tables) and refrigerants, but tables are also available for other substances like air, nitrogen, and carbon dioxide.

Organization of Thermodynamic Tables

Thermodynamic tables are generally structured into sections based on the phase of the substance:

1. Saturated Tables: These tables provide properties for saturated liquid and saturated vapor states at a given temperature or pressure. Saturated conditions occur when a substance is at its boiling point (or condensation point) for a given pressure.
2. Superheated Tables: These tables provide properties for the vapor phase at temperatures higher than the saturation temperature for a given pressure.
3. Compressed Liquid Tables: These tables provide properties for the liquid phase at pressures higher than the saturation pressure for a given temperature.

Key Columns in Thermodynamic Tables

1. Temperature (T): The temperature at which the properties are listed.
2. Pressure (P): The pressure at which the properties are listed.
3. Specific Volume (v): The volume per unit mass (m³/kg).
   • vf: Specific volume of saturated liquid.
   • vg: Specific volume of saturated vapor.
   • vfg: Difference between vg and vf (vg - vf).
4. Internal Energy (u): The internal energy per unit mass (kJ/kg).
   • uf: Specific internal energy of saturated liquid.
   • ug: Specific internal energy of saturated vapor.
   • ufg: Difference between ug and uf (ug - uf).
5. Enthalpy (h): The enthalpy per unit mass (kJ/kg).
   • hf: Specific enthalpy of saturated liquid.
   • hg: Specific enthalpy of saturated vapor.
   • hfg: Latent heat of vaporization (enthalpy of vaporization, hg - hf).
6. Entropy (s): The entropy per unit mass (kJ/kg·K).
   • sf: Specific entropy of saturated liquid.
   • sg: Specific entropy of saturated vapor.
   • sfg: Difference between sg and sf (sg - sf).

Using Saturated Water Tables

Saturated water tables are used to find the properties of water at saturation conditions. These tables can be either temperature-based or pressure-based.

Temperature-Based Tables

In temperature-based tables, the temperature is the primary entry point. For each temperature, the table lists the saturation pressure, specific volume of saturated liquid (vf) and saturated vapor (vg), internal energy of saturated liquid (uf) and saturated vapor (ug), enthalpy of saturated liquid (hf) and saturated vapor (hg), and entropy of saturated liquid (sf) and saturated vapor (sg).

Example:

From this table, if we know the temperature is 100°C and the water is saturated, we can directly find the saturation pressure (101.42 kPa) and other properties.

Pressure-Based Tables

In pressure-based tables, the pressure is the primary entry point. For each pressure, the table lists the saturation temperature, specific volume of saturated liquid (vf) and saturated vapor (vg), internal energy of saturated liquid (uf) and saturated vapor (ug), enthalpy of saturated liquid (hf) and saturated vapor (hg), and entropy of saturated liquid (sf) and saturated vapor (sg).

Example:

From this table, if we know the pressure is 100 kPa and the water is saturated, we can directly find the saturation temperature (99.61°C) and other properties.

Using Superheated Water Tables

Superheated water tables are used to find the properties of water when it is in the vapor phase and its temperature is higher than the saturation temperature for the given pressure. In these tables, temperature and pressure are typically the entry points, and the table lists specific volume (v), internal energy (u), enthalpy (h), and entropy (s).

Example:

From this table, if we know the pressure is 100 kPa and the temperature is 200°C, we can find the specific volume (2.1723 m³/kg), internal energy (2658.1 kJ/kg), enthalpy (2875.4 kJ/kg), and entropy (7.8343 kJ/kg·K).

Using Compressed Liquid Tables

Compressed liquid tables are used to find the properties of water when it is in the liquid phase and its pressure is higher than the saturation pressure for the given temperature. Since the properties of compressed liquids are not strongly dependent on pressure, often approximations are used, and the properties are taken from the saturated liquid tables at the given temperature.

Approximation Method:

• v(T, P) ≈ vf(T)
• u(T, P) ≈ uf(T)
• h(T, P) ≈ hf(T) + vf(T) * (P - Psat(T))
• s(T, P) ≈ sf(T)

Where:

• v(T, P), u(T, P), h(T, P), s(T, P) are the specific volume, internal energy, enthalpy, and entropy of the compressed liquid at temperature T and pressure P.
• vf(T), uf(T), hf(T), sf(T) are the specific volume, internal energy, enthalpy, and entropy of the saturated liquid at temperature T.
• Psat(T) is the saturation pressure at temperature T.

Determining Phase and Using Tables

To effectively use thermodynamic tables, one must first determine the phase of the substance. This can be done by comparing the given properties (temperature, pressure, specific volume, etc.) with the saturation properties.

1. Compressed Liquid: If P > Psat(T) or T < Tsat(P), the substance is a compressed liquid.
2. Saturated Mixture: If P = Psat(T) or T = Tsat(P), the substance is a saturated mixture. The quality x is used to determine the proportion of liquid and vapor.
3. Superheated Vapor: If P < Psat(T) or T > Tsat(P), the substance is a superheated vapor.

For a saturated mixture, the quality x is defined as the ratio of the mass of vapor to the total mass:

x = mvapor / (mliquid + mvapor)

The properties of a saturated mixture can be calculated using the quality x:

• v = vf + x * vfg
• u = uf + x * ufg
• h = hf + x * hfg
• s = sf + x * sfg

Example Problem

Consider water at a temperature of 150°C and a pressure of 500 kPa. Determine its phase and find its specific volume, internal energy, enthalpy, and entropy.

1. Determine the Phase:

   • From saturated water tables, at 150°C, Psat = 476.16 kPa.
   • Since P (500 kPa) > Psat (476.16 kPa), the water is in the compressed liquid phase.

2. Find the Properties:

   • Since compressed liquid tables are not always available, we use the approximation method:

     • vf at 150°C = 0.001091 m³/kg
     • uf at 150°C = 631.66 kJ/kg
     • hf at 150°C = 632.18 kJ/kg
     • sf at 150°C = 1.8418 kJ/kg·K

   • Correcting the enthalpy for pressure:

     • h(T, P) ≈ hf(T) + vf(T) * (P - Psat(T))
     • h ≈ 632.18 + 0.001091 * (500 - 476.16)
     • h ≈ 632.18 + 0.001091 * 23.84
     • h ≈ 632.21 kJ/kg

   • So, the approximate properties are:

     • v ≈ 0.001091 m³/kg
     • u ≈ 631.66 kJ/kg
     • h ≈ 632.21 kJ/kg
     • s ≈ 1.8418 kJ/kg·K

Applications of Thermodynamic Properties

Thermodynamic properties are essential in a wide range of engineering applications. Some notable examples include:

1. Power Generation: In power plants, the properties of water and steam are crucial for designing turbines, boilers, and condensers. The efficiency of a power plant depends heavily on the accurate determination of these properties.
2. Refrigeration and Air Conditioning: Refrigerants are used in cooling systems to transfer heat. Understanding the thermodynamic properties of refrigerants helps in designing efficient and effective refrigeration cycles.
3. Chemical Processes: Many chemical reactions involve changes in temperature, pressure, and phase. Thermodynamic properties are used to calculate the heat and work involved in these processes and to design reactors and separation units.
4. HVAC Systems: In heating, ventilation, and air conditioning systems, the properties of air and water are used to design and optimize the performance of the systems.
5. Engine Design: In internal combustion engines, the properties of fuel and air mixtures are essential for understanding the combustion process and designing efficient engines.

Advanced Concepts and Considerations

Interpolation

In many cases, the exact temperature or pressure you need is not listed in the thermodynamic tables. In such situations, interpolation is necessary to estimate the property values. Linear interpolation is the most common method:

• y = y1 + (x - x1) * ((y2 - y1) / (x2 - x1))

Where:

• x is the known value (e.g., temperature or pressure)
• y is the property you want to find
• x1, y1 are the known values from the table just below x
• x2, y2 are the known values from the table just above x

Equations of State

For situations where thermodynamic tables are not available or for more accurate calculations, equations of state can be used. Equations of state are mathematical relationships between pressure, volume, and temperature. Some common equations of state include:

1. Ideal Gas Law: PV = nRT (where n is the number of moles, and R is the ideal gas constant)
2. Van der Waals Equation: (P + a(n/V)²) * (V - nb) = nRT (where a and b are substance-specific constants)
3. Redlich-Kwong Equation: P = (RT / (v - b)) - (a / (T^0.5 * v * (v + b))) (where a and b are substance-specific constants)

Software and Online Resources

Modern engineering practice often involves the use of software and online resources for accessing thermodynamic properties. Programs like MATLAB, Engineering Equation Solver (EES), and online databases provide convenient access to a wide range of property data for various substances.

Common Mistakes and How to Avoid Them

Using thermodynamic tables can sometimes be tricky, and several common mistakes can lead to incorrect results. Here are some common pitfalls and how to avoid them:

1. Incorrect Phase Identification:

   • Mistake: Misidentifying the phase of the substance (e.g., treating a compressed liquid as a saturated liquid).
   • Solution: Always compare the given properties with saturation properties to correctly determine the phase.

2. Using the Wrong Table:

   • Mistake: Using a saturated table when a superheated table is needed, or vice versa.
   • Solution: Double-check the phase and choose the appropriate table.

3. Incorrect Interpolation:

   • Mistake: Making errors during interpolation, such as using the wrong formula or incorrect values.
   • Solution: Use a systematic approach for interpolation and double-check your calculations.

4. Forgetting Units:

   • Mistake: Ignoring or mixing up units (e.g., using °C instead of K).
   • Solution: Always pay close attention to units and ensure consistency.

5. Misunderstanding Quality (x):

   • Mistake: Incorrectly applying the quality x in saturated mixture calculations.
   • Solution: Ensure you understand that x represents the fraction of vapor in the mixture and use the correct formulas.

Conclusion

Thermodynamic properties of pure substances are fundamental to many engineering disciplines. Mastery of using thermodynamic tables and understanding the underlying concepts is crucial for accurate and efficient analysis and design of thermal systems. By understanding the organization of these tables, correctly identifying the phase of the substance, and avoiding common mistakes, engineers and scientists can effectively utilize these tools to solve complex thermodynamic problems. From power generation to refrigeration and chemical processes, the applications are vast and essential for modern technology.