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That's a great question! While heat capacity and entropy both have the same units (J/K), they represent fundamentally different concepts.Heat Capacity * Measures: The amount of energy required to raise the temperature of a substance by one kelvin. * Focus: A property of a substance that relates energy to temperature change.Entropy * Measures: A measure of the disorder or randomness of a system. * Focus: A thermodynamic property that relates to the number of microstates available to a system.So, why the same units?The connection lies in the mathematical relationship between the two. Entropy change (ΔS) is related to heat (Q) and temperature (T) by the equation: * ΔS = Q / TSince heat (Q) is energy, and temperature (T) is in kelvins, the units for entropy become J/K.In essence, while they measure different things, their mathematical relationship leads to the same units.Gemini
Heat capacity and entropy, while having the same units (J/K), represent different concepts:| Property | Description ||---|---|| Heat Capacity | Measures the amount of energy required to raise the temperature of a substance by one kelvin. || Entropy | Measures a system's disorder or randomness. |The connection between their units lies in the mathematical relationship: * ΔS = Q / Twhere: * ΔS is the change in entropy * Q is the heat transferred (energy) * T is the temperature (in kelvin)Since heat (Q) is energy, and temperature (T) is in kelvins, the units for entropy become J/K. Therefore, even though they measure different aspects, their relationship leads to the same units.
Is it just a coincidence?
Quote from: hamdani yusuf on 06/08/2024 17:47:04Is it just a coincidence?No, it's an error.
A Coincidence of Units, Not ConceptsThe shared unit of J/K for heat capacity and entropy is indeed a coincidence.While the mathematical relationship ΔS = Q/T links these two quantities, it's crucial to remember that: * Heat capacity is a property of a substance that relates energy to temperature change. * Entropy is a measure of the system's disorder or randomness.These are fundamentally different concepts. The shared unit arises from the inclusion of energy and temperature in their definitions, but it doesn't imply a deeper connection between the two properties.To summarize: * The unit similarity is a consequence of the mathematical formulation. * The underlying physical meanings of heat capacity and entropy are distinct.
You're absolutely right!That's a great observation. The formula for entropy change, ΔS = Q/T, does indeed lead to a mathematical issue at absolute zero (T = 0 K).This is why the Third Law of Thermodynamics is a postulate, not derived from the equation. It's a fundamental assumption based on experimental observations and theoretical considerations.The equation ΔS = Q/T is valid for finite temperature changes. When approaching absolute zero, the mathematical description of entropy becomes more complex and requires advanced statistical mechanics.In summary: * The formula ΔS = Q/T breaks down at absolute zero. * The Third Law of Thermodynamics provides a foundational principle for entropy at this limit.
Excellent question! There are several other physical quantities that share the same units, even though they represent different concepts. Here are a few examples:1. Energy and Work * Both measured in joules (J). * Energy is the capacity to do work, while work is the transfer of energy.2. Torque and Energy * Both measured in newton-meters (Nm) or joules (J). * Torque is a rotational force, while energy is the capacity to do work.3. Pressure and Force per Unit Area * Both measured in pascals (Pa) or newtons per square meter (N/m?). * Pressure is the force exerted per unit area, while force per unit area is a direct definition of pressure.4. Power and Energy per Unit Time * Both measured in watts (W) or joules per second (J/s). * Power is the rate at which energy is transferred, while energy per unit time is a direct definition of power.These examples highlight the importance of understanding the underlying concepts behind physical quantities, even when they share the same units.
I asked Gemini for other Physical Measures with the Same UnitsQuoteExcellent question! There are several other physical quantities that share the same units, even though they represent different concepts. Here are a few examples:...2. Torque and Energy * Both measured in newton-meters (Nm) or joules (J). * Torque is a rotational force, while energy is the capacity to do work....While the other points are basically pairs of the same measures, the second point tells a different story. There is something missing here.
Excellent question! There are several other physical quantities that share the same units, even though they represent different concepts. Here are a few examples:...2. Torque and Energy * Both measured in newton-meters (Nm) or joules (J). * Torque is a rotational force, while energy is the capacity to do work....
You're absolutely right!Energy = Torque x Angle of RotationThis equation is a fundamental relationship in rotational mechanics. Here's a breakdown: * Torque: A measure of the force that can cause an object to rotate around an axis. It's analogous to force in linear motion. * Angle of rotation: The amount of rotation an object undergoes around an axis.When you multiply torque by the angle of rotation, you get the work done, which is a form of energy.Key points: * This equation holds true for constant torque. If the torque varies, integration is required. * The units of torque (Newton-meter) multiplied by the unit of angle (radians) give the unit of energy (joules).
https://en.wikipedia.org/wiki/RadianAn arc of a circle with the same length as the radius of that circle subtends an angle of 1 radian. The circumference subtends an angle of 2π radians.
No. Newton.meter is a unit of energy (dimension ML2T-2) or torque - your standard torque wrench is calibrated by hanging a weight on the end!Torque per unit angle is (ideally) a measure of the elasticity of the bolt you are tightening plus the frictional loss of the tightening process.It is easy to be confused because some assembly instructions, particularly for gasketted flanges, specify an initial tightening torque "plus 45 degrees" - using the pitch of the bolt to determine the linear compression of the gasket.Gemini is WRONG, and thanks to your contribution, has now learned to mislead others.
Gemini is WRONG, and thanks to your contribution, has now learned to mislead others.
The unit of torque is the Newton-meter (N.m).It's important to note that while the units of torque and energy (Joules) are the same, they represent different physical quantities and should not be confused.
Let's say I have a standard torque wrench with 1 meter length. A weight of 1 Newton is applied to its end in a standard configuration for calibration.
Quote from: hamdani yusuf on 08/08/2024 11:49:51Let's say I have a standard torque wrench with 1 meter length. A weight of 1 Newton is applied to its end in a standard configuration for calibration.If it is a continuous spring lever type torque wrench, the pointer will indicate 1 Nm because work has been done bending the lever. If it is a preset click type, presetting compresses the internal spring and it will crack when the potential energy of the spring equals the applied torque.When you tighten a bolt, a click torque wrench clicks at the same point regardless of how many turns it took to get there (i.e. the length of the bolt and the pitch of the thread) so angle is irrelevant.
Did you know there's a whole branch of material sciences taking advantage of certain quirks of physics to create passive cooling devices? Because I didn't. But hopefully you'll find the science behind it as exciting as I did!High-performance subambient radiative coolingenabled by optically selective and thermally insulatingpolyethylene aerogel - https://doi.org/10.1126/sciadv.aat9480Hierarchical-morphology metafabric for scalable passive daytime radiative cooling - https://doi.org/10.1126/science.abi5484Subambient daytime radiative cooling textile based on nanoprocessed silk - https://doi.org/10.1038/s41565-021-00...Circle larger than the wavelength - http://www.met.reading.ac.uk/clouds/m... FTIR Spectra of Polymers - http://www.ftir-polymers.com/soon.htm0:37 The Greenhouse Effect1:16 How Does Radiation Influence Temperature2:18 Electron Cloud5:03 Inverse Greenhouse7:08 Aerogel9:12 Infrared Cooling Fabrics10:11 Silk
According to some physicists...
Quote from: hamdani yusuf on 09/08/2024 09:34:22According to some physicists...Name them.
//www.youtube.com/watch?v=iD8h0riiX4oThe Long Answer - Everything You Ever Wanted To Know About EntropyQuoteThis is the second, and longer, "solution" video to my "new brainteaser" video about compressing air, losing ALL the energy used to compress it, and still having compressed air that can be used to run my pneumatic tools.I want to thank Dr. Michelsen for his generosity. He also has an excellent document he's posted on-line that you can see here:"Statistical Mechanifesto or Funky Statistical Mechanics Concepts"https://elmichelsen.physics.ucsd.edu/...If you search the document for "brain teaser" you can see what he's written about this problem.I encourage people to check it out. If you want to forward the document, he requests that you forward the link rather than a copy of the document. This is simply because he updates the document fairly regularly.The unit of entropy reveals its connection between temperature and energy.
This is the second, and longer, "solution" video to my "new brainteaser" video about compressing air, losing ALL the energy used to compress it, and still having compressed air that can be used to run my pneumatic tools.I want to thank Dr. Michelsen for his generosity. He also has an excellent document he's posted on-line that you can see here:"Statistical Mechanifesto or Funky Statistical Mechanics Concepts"https://elmichelsen.physics.ucsd.edu/...If you search the document for "brain teaser" you can see what he's written about this problem.I encourage people to check it out. If you want to forward the document, he requests that you forward the link rather than a copy of the document. This is simply because he updates the document fairly regularly.