Equation of State and Liquid Helium

Topic: Equation of State and Liquid Helium Presented by: Shahid Riaz Contents :  What is Equation of State ?  Types of Equation of State  Uses and Applications of Equation of State  What is Liquid Helium  Types of Liquid Helium  Properties of Liquid Helium  Uses and Applications  Conclusion What is Equation of State ? Introduction;  The Equation of State (EoS) describes the relationship between thermodynamic variables such as:  Pressure (P)  Volume (V)  Temperature (T)  It is fundamental in thermodynamics, statistical mechanics, and material science.  Helps predict behavior of gases, liquids, and solids under different conditions. Scientists Behind Equation of State :  🔷 Step-by-Step Derivation 1. Robert Boyle (Boyle’s Law) At constant temperature: 𝟏 𝑷∝ 𝑽  This means: 𝑷𝑽 = constant 2. Jacques Charles (Charles’s Law) At constant pressure: 𝑽∝𝑻  So:  𝑽 𝑻 = constant 3. Amedeo Avogadro (Avogadro’s Law) At constant temperature and pressure: 𝑽∝𝒏 So:  𝑽 𝒏 = constant 🔷 Combine All Three Laws Now combine: 𝑽∝𝑻 , 𝑽∝𝒏 𝒂𝒏𝒅 𝑽 ∝ 𝟏 𝑷 👉Putting together: 𝑽∝ 𝒏𝑻 𝑷  Remove proportionality by adding constant 𝑅:  𝑷𝑽 = 𝒏𝑹𝑻  Solved Forms of Equation :  For Pressure: 𝑷= 𝒏𝑹𝑻 𝑽 𝑽= 𝒏𝑹𝑻 𝑷  Volume:  Temperature: 𝑻= 𝑷𝑽 𝒏𝑹 Types of Equation of State 1- Ideal Gas Equation 2- Van der Waals Equation (Real Gas) 3- Virial Equation 1. Ideal Gas Equation Equation ; PV=nRT Explanation;  This is the simplest equation of state.  Assumptions:  Gas molecules have no volume.  No intermolecular forces exist.  Valid under:  Low pressure  High temperature Key Point;  Works well for theoretical calculations but fails for real gases at extreme conditions. 2. Van der Waals Equation (Real Gas)  Van der Waals equation is not derived from simple laws like the ideal gas law. It is obtained by modifying the ideal gas equation using physical corrections for real gases. Ideal Gas Equation  𝑷𝑽 = 𝒏𝑹𝑻 🔷 Volume Correction (Finite Size of Molecules) • Real gas molecules occupy space • So actual free volume is less than container volume • Corrected volume: • 𝑽real = 𝑽 − 𝒃 • 𝑏 =volume occupied by molecules 🔷 Pressure Correction (Intermolecular Attraction)  Molecules attract each other  This reduces the force on container walls • So observed pressure is less than actual pressure • Corrected pressure: 𝒂 • 𝑷real = 𝑷 + 𝟐 𝑽 • 𝑎 =measure of intermolecular attraction Substitute Corrections into Ideal Gas Equation  Replace:  𝑷→𝑷+ 𝒂 𝑽𝟐  𝑽→𝑽−𝒃  Final equation: 𝑷+ 𝒂 𝑽𝟐 𝑽 − 𝒃 = 𝒏𝑹𝑻  “The Van der Waals equation is derived by modifying the ideal gas law. We correct volume because molecules have size, and we correct pressure because molecules attract each other. These corrections lead to a more accurate equation for real gases.” 3. Virial Equation of State 𝑷𝑽 𝒏𝑹𝑻 𝑩 𝑽 =𝟏+ + 𝑪 𝑽𝟐 + 𝑫 𝑽𝟑 +⋯ For an ideal gas:  𝑷𝑽 = 𝒏𝑹𝑻 ⇒ 𝑷𝑽 𝒏𝑹𝑻 =𝟏 In real gases  “Let’s correct the ideal gas equation by adding extra terms”  These corrections depend on volume (V) So we write:  𝑷𝑽 𝒏𝑹𝑻 = 𝟏 + corrections Use Series Expansion  The correction is written like a mathematical series (similar idea to Taylor expansion) Final form:  𝑷𝑽 𝒏𝑹𝑻 𝑩 𝑽 =𝟏+ + 𝑪 𝑽𝟐 + 𝑫 𝑽𝟑 +⋯ Where do B, C, D come from?  These are Virial coefficients  They depend on temperature Physical Meaning (Very Important)  𝐵→ interaction between two molecules  𝐶→ interaction between three molecules  𝐷→ interaction of many molecule 🔷 Why this Equation is Important ?  Gives very accurate results  Used in advanced physics and chemistry  Better than Van der Waals when more terms are included  “The Virial equation is obtained by expanding the ideal gas equation and adding correction terms. These terms account for interactions between molecules, making the equation more accurate for real gases.” Uses of Equation of State (EoS) The Equation of State is mainly used to calculate unknown thermodynamic quantities. 1. Determining Gas Properties Used to calculate:  Pressure (P)  Volume (V)  Temperature (T) Example:  Using 𝒏𝑹𝑻 𝑷= 𝑽 2. Predicting Gas Behavior  Helps determine whether a gas behaves:  Ideally  Or as a real gas  Important in high pressure systems 3. Thermodynamic Calculations Used in:  Internal energy calculations  Work done by gases  Heat transfer analysis 🔷 Applications of Equation of State (EoS) 1. Application in Engineering Systems  Equation of State is used to design machines like compressors and engines.  It helps engineers calculate how pressure, volume, and temperature change during operation. 2. Application in Gas Storage  It is used in gas cylinders and storage tanks.  EoS helps determine how gases behave under high pressure for safe storage. 3. Application in Thermodynamic Processes  Used to study processes like expansion and compression of gases.  It helps calculate work done and energy changes in systems. 4. Application in Refrigeration and Air Conditioning  EoS helps in understanding phase changes of gases into liquids.  It is important for designing cooling systems like refrigerators and ACs. 5. Application in Petroleum Industry  Used to study behavior of natural gas and crude oil in reservoirs.  Helps in extraction, refining, and transportation of petroleum products . Liquid Helium  Liquid helium is helium gas that has been cooled to a very low temperature until it turns into a liquid.  It becomes liquid at about 4.2 Kelvin (−269°C).  It is the coldest liquid known.  At even lower temperature (below 2.17 K), it shows special behavior called superfluidity, where it can flow without resistance.  👉 Simple one-line definition: Liquid helium is helium in liquid form at extremely low temperature, used for cooling and scientific research. Why Helium is Special ? Helium atoms:  Are very small  Have very weak intermolecular forces Because of this:  It does not solidify easily  Requires high pressure to freeze  Helium becomes solid at extremely low temperatures (0 K) and high pressure (25 atmospheres or more). At normal pressure, helium does not freeze due to strong quantum effects. 🔹 Types of Liquid Helium 1. Helium I (normal liquid )  Temperature: 4.2 K to 2.17 K  Properties:  Normal liquid  Has viscosity  Behaves like classical fluids 2. Helium II (Superfluid Phase)  Temperature: Below 2.17 K  Known as superfluid Superfluidity (Important Concept) Definition:  A state where liquid flows with zero viscosity (no friction) Key Features  Flows without energy loss  Extremely high thermal conductivity  Does not obey classical physics Reason  Explained by quantum mechanics  At very low temperature, atoms behave like a single quantum system Properties of Liquid Helium:  Liquid helium has a very low boiling point of 4.2 K (−268.9°C) at normal pressure.  It has no normal freezing (melting) point because it does not solidify at atmospheric pressure.  It shows very low density compared to other liquids.  It has almost zero viscosity in the superfluid state.  It has very high thermal conductivity and transfers heat very quickly.  It shows quantum effects, especially superfluidity below 2.17 K. 🔷 Uses of Liquid Helium 1. Cooling in MRI Machines  Liquid helium is used to cool superconducting magnets in MRI machines.  It keeps the temperature extremely low so the magnets work efficiently. 2. Superconductivity Applications  It is used to maintain very low temperatures required for superconductors.  This allows materials to conduct electricity with zero resistance. 3. Space and Rocket Technology  Liquid helium is used in rockets to cool fuel systems and instruments.  It also helps in maintaining stable low temperatures in space missions. 🔹 Applications of Liquid Helium 1. Quantum Computing  Maintains ultra-low temperatures 2. Particle Accelerators  Cooling powerful magnets 3. Cryogenics  Used in extreme low-temperature systems 4. Nuclear Research  Used in advanced experiments Final Conclusion :  The Equation of State provides a mathematical description of matter.  It is essential in:  Engineering  Industry  Scientific research  Liquid Helium is unique because:  It shows quantum effects at macroscopic level  Exhibits superfluidity  👉 Both topics are fundamental in modern physics and advanced technology