12.1 Laws of thermodynamics and molecular interpretation

Thermodynamics is all about energy and how it moves around. It's like understanding the rules of a cosmic game where heat, work, and energy are the players. These laws explain why things happen the way they do in our world.

At the molecular level, thermodynamics is about particles dancing and interacting. It tells us why ice melts, gases expand, and why you can't un-mix your coffee after adding cream. It's the science behind why things naturally get messy over time.

Molecular Basis of Thermodynamics

First Law of Thermodynamics and Energy Conservation

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• The first law of thermodynamics states the change in internal energy of a system (ΔU) equals the heat (Q) added to the system minus the work (W) done by the system on its surroundings: $ΔU = Q - W$
• Internal energy (U) at the molecular level is the sum of the kinetic and potential energies of all particles in a system
  • Kinetic energy is associated with particle motion
  • Potential energy arises from intermolecular forces and interactions (van der Waals forces, hydrogen bonding)
• Heat (Q) is the transfer of energy between a system and its surroundings due to a temperature difference
  • At the molecular level, heat transfer involves the exchange of kinetic energy between particles through collisions or the transfer of vibrational, rotational, or electronic energy
  • Examples: heat transfer from a hot object to a cold object, energy transfer during phase changes (melting, vaporization)
• Work (W) is the energy transfer that occurs when a system changes its volume against an external pressure
  • At the molecular level, work is performed when particles collectively move against an external force, such as during expansion or compression
  • Examples: work done by a gas during expansion, work required to compress a spring
• The first law of thermodynamics implies energy conservation, meaning energy cannot be created or destroyed, only converted from one form to another or transferred between a system and its surroundings

Molecular Interpretation of Internal Energy and Heat Transfer

• Internal energy changes (ΔU) can result from heat transfer (Q) or work (W) done on or by the system
  • Heat added to a system (positive Q) increases the kinetic energy of particles, raising the system's temperature and internal energy
  • Work done by the system (positive W) decreases the system's internal energy, as energy is transferred to the surroundings
• Heat capacity is the amount of heat required to raise the temperature of a substance by one degree
  • At the molecular level, heat capacity depends on the number of ways in which particles can absorb energy (translational, rotational, vibrational, and electronic modes)
  • Substances with more complex molecular structures or higher molecular weights tend to have higher heat capacities
• Specific heat is the heat capacity per unit mass of a substance
  • Water has a high specific heat due to its strong hydrogen bonding, which allows it to absorb a large amount of energy without significantly increasing its temperature
  • This property makes water an excellent coolant in industrial processes and helps regulate Earth's climate

Entropy and Spontaneous Processes

Second Law of Thermodynamics and Entropy

• The second law of thermodynamics states that the total entropy of an isolated system always increases over time
  • Entropy is a measure of the disorder or randomness of a system
  • At the molecular level, entropy is related to the number of microstates (different arrangements of particles) that correspond to a given macrostate (observable properties of the system, such as temperature, pressure, and volume)
• A system with a higher number of microstates has greater entropy
  • As particles move and interact, they naturally tend towards arrangements that maximize the number of microstates, increasing the system's entropy
  • Examples: gas particles spreading out to fill a container, ice melting into water (more disordered state)
• The second law of thermodynamics explains why heat flows from hot to cold objects, gases expand to fill their containers, and chemical reactions proceed towards equilibrium
  • These processes increase the overall entropy of the system and its surroundings
  • Example: a drop of ink dispersing in water (increasing disorder)

Spontaneous Processes and Molecular Entropy

• Spontaneous processes occur without external intervention and always proceed in the direction of increasing total entropy (system + surroundings)
  • At the molecular level, spontaneous processes involve the system moving towards a more probable state with a higher number of microstates
  • Examples: salt dissolving in water, iron rusting in the presence of oxygen and water
• Gibbs free energy (G) is a thermodynamic quantity that determines the spontaneity of a process at constant temperature and pressure
  • Gibbs free energy is defined as: $G = H - TS$, where H is enthalpy, T is temperature, and S is entropy
  • A negative change in Gibbs free energy (ΔG < 0) indicates a spontaneous process, while a positive change (ΔG > 0) indicates a non-spontaneous process
• The second law of thermodynamics and the concept of entropy provide a molecular explanation for the direction of spontaneous processes and the arrow of time
  • The universe as a whole tends towards a state of maximum entropy, which is a consequence of the statistical behavior of particles and their tendency to maximize disorder

Molecular Implications of Zeroth and Third Laws

Zeroth Law and Thermal Equilibrium

• The zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other
  • Thermal equilibrium occurs when there is no net heat transfer between systems
  • At the molecular level, thermal equilibrium is achieved when the average kinetic energy of particles in two systems is equal, resulting in the same temperature
• The zeroth law provides the basis for measuring temperature and constructing temperature scales, such as the Kelvin scale, which is based on the concept of absolute zero
  • Temperature is a measure of the average kinetic energy of particles in a system
  • Higher temperatures correspond to faster particle motion and greater kinetic energy
• When systems with different temperatures are brought into contact, heat flows from the higher-temperature system to the lower-temperature system until thermal equilibrium is reached
  • At the molecular level, this heat transfer occurs through collisions between particles, with faster-moving particles in the higher-temperature system transferring energy to slower-moving particles in the lower-temperature system
  • Example: a hot metal object cooling down when placed in a room-temperature environment

Third Law and Absolute Zero

• The third law of thermodynamics states that the entropy of a perfect crystal at absolute zero (0 K) is zero
  • As the temperature approaches absolute zero, the entropy of a system approaches a constant minimum value
  • At the molecular level, a perfect crystal at absolute zero has all its particles arranged in a highly ordered lattice structure, with minimal disorder or randomness, corresponding to a single microstate and zero entropy
• In reality, reaching absolute zero is impossible, as it would require an infinite number of steps and an infinite amount of energy
  • The third law provides a theoretical limit for the lowest possible entropy of a system
  • As the temperature approaches absolute zero, the heat capacity of a system also approaches zero, indicating that the system cannot absorb or release any more energy
• The third law has important implications for the behavior of materials at extremely low temperatures
  • Superconductors, materials that conduct electricity with zero resistance, often exhibit their unique properties near absolute zero
  • The study of materials at ultra-low temperatures helps scientists understand the fundamental properties of matter and develop new technologies (quantum computing, ultra-sensitive sensors)