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- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(Fleming)/05%3A_The_Second_Law/5.03%3A_EntropyThe page discusses the Carnot engine and its relationship with temperature and efficiency. It explains how the total heat transferred in the cycle is derived, showing that heat (q) is not a state func...The page discusses the Carnot engine and its relationship with temperature and efficiency. It explains how the total heat transferred in the cycle is derived, showing that heat (q) is not a state function due to its net change around a closed cycle being non-zero. However, when considering the sum of q/T, it results in zero, which aligns with the behavior of a state function.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/14%3A_Nuclear_Magnetic_Resonance_Spectroscopy/14.03%3A_Proton_NMR_Spectrometers_Operate_at_Frequencies_Between_60_MHz_and_750_MHzThis page discusses the Heisenberg Uncertainty Principle, established by Werner Heisenberg in the mid-1920s. It states that more precise measurement of an electron's position results in greater uncert...This page discusses the Heisenberg Uncertainty Principle, established by Werner Heisenberg in the mid-1920s. It states that more precise measurement of an electron's position results in greater uncertainty in its momentum, due to the wave nature of matter. This principle illustrates fundamental limits in quantum measurements by mathematically expressing the relationship between uncertainties in position and momentum.
- https://chem.libretexts.org/Courses/Western_Washington_University/Biophysical_Chemistry_(Smirnov_and_McCarty)/01%3A_Biochemical_Thermodynamics/1.05%3A_The_Boltzmann_Distribution_and_the_Statistical_Definition_of_EntropyIn this chapter we introduce the statistical definition of entropy as formulated by Boltzmann. This allows us to consider entropy from the perspective of the probabilities of different configurations ...In this chapter we introduce the statistical definition of entropy as formulated by Boltzmann. This allows us to consider entropy from the perspective of the probabilities of different configurations of the constituent interacting particles in an ensemble. This conception of entropy led to the development of modern statistical thermodynamics. For systems that can exchange thermal energy with the surroundings, the equilibrium probability distribution will be the Boltzmann distribution.
- https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/05%3A_Electrons_in_Atoms/5.03%3A_Quantization_of_EnergyThis page clarifies that "quantum leap" refers to minor changes in an electron's position, not significant breakthroughs. It highlights Max Planck's discovery that energy emits in discrete units calle...This page clarifies that "quantum leap" refers to minor changes in an electron's position, not significant breakthroughs. It highlights Max Planck's discovery that energy emits in discrete units called quanta, opposing classical physics' continuous energy view. A quantum is the smallest energy change for an atom, defined by Planck's constant h=6.626×10−34J⋅s. This principle is fundamental for understanding energy behavior at the atomic level.
- https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/05%3A_Electrons_in_Atoms/5.09%3A_Quantum_MechanicsThis page delves into quantum mechanics, highlighting the dual wave-particle nature of atomic and subatomic particles. It contrasts quantum mechanics with classical mechanics, focusing on discrete ene...This page delves into quantum mechanics, highlighting the dual wave-particle nature of atomic and subatomic particles. It contrasts quantum mechanics with classical mechanics, focusing on discrete energy changes (quanta) and the fundamental uncertainty in electron positioning, which is addressed through probabilities. Prominent physicists like Niels Bohr and Richard Feynman stressed the baffling aspects of quantum theory, emphasizing its challenge to traditional concepts in physics.
- https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/03%3A_Measurements/3.07%3A_Temperature_and_Temperature_ScalesThis page explains temperature as a measure of average kinetic energy, describing the Fahrenheit, Celsius, and Kelvin scales, including their freezing and boiling points. It notes that Celsius and Kel...This page explains temperature as a measure of average kinetic energy, describing the Fahrenheit, Celsius, and Kelvin scales, including their freezing and boiling points. It notes that Celsius and Kelvin are related by 273 and emphasizes the simplicity of conversions between these scales. Additionally, it mentions the historical development and relevance of these temperature scales in the field of chemistry.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(Fleming)/01%3A_The_Basics/1.05%3A_Work_and_EnergyThe page discusses fundamental concepts of thermodynamics, focusing on temperature, pressure, volume, and energy exchange through work and heat. It highlights the importance of energy in modern societ...The page discusses fundamental concepts of thermodynamics, focusing on temperature, pressure, volume, and energy exchange through work and heat. It highlights the importance of energy in modern society and introduces kinetic and potential energy. Hooke???s Law is discussed as an example of energy conversion between kinetic and potential forms. Work is defined as energy expenditure to move an object against a force, with applications illustrated in examples like gas expansion.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(Fleming)/03%3A_First_Law_of_Thermodynamics/3.01%3A_Prelude_to_ThermodynamicsThe text discusses thermodynamics, highlighting a quote from Albert Einstein praising the simplicity and universality of its laws. Thermodynamics is the study of energy flow in systems and the univers...The text discusses thermodynamics, highlighting a quote from Albert Einstein praising the simplicity and universality of its laws. Thermodynamics is the study of energy flow in systems and the universe, often involving complex relationships related to basic energy principles. It plays a crucial role in processes like powering cars, electronics, and heating.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(Fleming)/05%3A_The_Second_Law/5.08%3A_Adiabatic_CompressibilityChapter 4 discusses isothermal compressibility, κT, an important thermodynamic quantity that aids in understanding various thermodynamic processes. The text explores historical insights by I...Chapter 4 discusses isothermal compressibility, κT, an important thermodynamic quantity that aids in understanding various thermodynamic processes. The text explores historical insights by Isaac Newton, who miscalculated the speed of sound due to an assumption of isothermal compression, rather than adiabatic compression as later corrected by Pierre-Simon Laplace.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/25%3A_Solutions_II_-_Nonvolatile_Solutes/25.08%3A_Homework_ProblemsThis page discusses the mid-1920s development of the uncertainty principle by physicist Werner Heisenberg, which states that the precision of a quantum particle's position and momentum is inherently l...This page discusses the mid-1920s development of the uncertainty principle by physicist Werner Heisenberg, which states that the precision of a quantum particle's position and momentum is inherently limited. This principle reveals that decreasing uncertainty in one aspect increases it in the other, stemming from the wave nature of matter. An exercise included illustrates the differences in positional uncertainty between a baseball and an electron.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/03%3A_The_Schrodinger_Equation_and_a_Particle_in_a_Box/3.08%3A_The_Uncertainty_Principle_-_Estimating_Uncertainties_from_WavefunctionsThis page explains Heisenberg's Uncertainty Principle, highlighting the relationship between position and momentum uncertainties, which cannot be measured simultaneously. It discusses calculations usi...This page explains Heisenberg's Uncertainty Principle, highlighting the relationship between position and momentum uncertainties, which cannot be measured simultaneously. It discusses calculations using a Gaussian wavefunction, confirming that the product of uncertainties adheres to the principle. An exercise is presented involving a particle in a one-dimensional box to further explore these concepts.
