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Pressure and Volume in an Adiabatic Process01:27

Pressure and Volume in an Adiabatic Process

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Free expansion of a gas is an adiabatic process. However, there are few differences between free expansion and adiabatic expansion. During free expansion, no work is done, and there is no change in internal energy. But, for an adiabatic expansion, work is done, and there is a change in internal energy. During an adiabatic process, the relation between the pressure and volume is obtained from the condition for the adiabatic process, that is, 
2.9K
Adiabatic Processes for an Ideal Gas01:18

Adiabatic Processes for an Ideal Gas

3.2K
When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...
3.2K
Work Done in an Adiabatic Process01:20

Work Done in an Adiabatic Process

3.4K
Consider the adiabatic compression of an ideal gas in the cylinder of an automobile diesel engine. The gasoline vapor is injected into the cylinder of an automobile engine when the piston is in its expanded position. The temperature, pressure, and volume of the resulting gas-air mixture are 20 °C, 1.00 x 105 N/m2, and 240 cm3 , respectively. The mixture is then compressed adiabatically to a volume of 40 cm3. Note that, in the actual operation of an automobile engine, the compression is not...
3.4K
Bernoulli's Equation: Problem Solving01:16

Bernoulli's Equation: Problem Solving

1.4K
A Venturi meter is essential for measuring fluid flow rates in pipelines. It utilizes the relationship between fluid velocity and pressure described by Bernoulli's equation. When installed in a sewage system, the Venturi meter accurately determines the wastewater flow rate by measuring pressure differences.
The first step is to compute the cross-sectional areas of the pipe and the Venturi throat to analyze the pressure difference indicated by the pressure gauge. Next, the continuity...
1.4K
Efficiency of The Carnot Cycle01:16

Efficiency of The Carnot Cycle

2.8K
The hypothetical Carnot cycle consists of an ideal gas subjected to two isothermal and two adiabatic processes. Since the internal energy of an ideal gas depends only on its temperature, which is the same before and after the completion of the Carnot cycle, there is no change in its internal energy. Hence, using the first law of thermodynamics, the total heat exchanged by the ideal gas equals the total work done. Thus, we can quantify the efficiency of the Carnot cycle via the heat exchanged...
2.8K
Rectangular and Triangular Pulse Function01:19

Rectangular and Triangular Pulse Function

976
The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
976

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Related Experiment Video

Updated: Aug 28, 2025

Evolution of Staircase Structures in Diffusive Convection
07:28

Evolution of Staircase Structures in Diffusive Convection

Published on: September 5, 2018

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Analytical solution for the inverting pulses with constant adiabaticity.

Konstantin L Ivanov1, Alexander V Snadin1, Alexei S Kiryutin1

  • 1International Tomography Center, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia; Novosibirsk State University, Novosibirsk 630090, Russia.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|September 18, 2022
PubMed
Summary

Researchers found an exact solution for inverting spin-1/2 pulses with constant adiabaticity. This method offers sharp inversion selectivity for Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR), and Magnetic Resonance Imaging (MRI).

Keywords:
Exact solution for constant adiabaticityFrequency-swept pulsesInverting pulsesSpin dynamics

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Area of Science:

  • Quantum Control
  • Magnetic Resonance Spectroscopy
  • Applied Physics

Background:

  • Adiabatic pulses are crucial for precise spin manipulation in magnetic resonance.
  • Maintaining constant adiabaticity during inversion pulses is challenging but essential for selectivity.
  • Existing methods like the hyperbolic tangent-hyperbolic secant pulse have limitations.

Purpose of the Study:

  • To derive an exact analytical solution for spin-1/2 inversion pulses with constant adiabaticity.
  • To establish the relationship between microwave field frequency and amplitude for constant adiabaticity.
  • To construct novel pulses based on the derived solution and evaluate their performance.

Main Methods:

  • Derivation of an analytical solution for spin-1/2 inversion pulses.
  • Mathematical analysis of the relationship between resonant field frequency and amplitude.
  • Numerical construction and simulation of new pulse sequences.
  • Comparison with established Electron Paramagnetic Resonance (EPR) pulse methods.

Main Results:

  • An exact solution was found for inverting pulses with constant adiabaticity for spin-1/2.
  • An analytical relationship was established between time-varying microwave field frequency and amplitude.
  • New pulses with constant adiabaticity were constructed, demonstrating sharp inversion selectivity.
  • Performance was compared favorably to existing hyperbolic tangent-hyperbolic secant pulse methods.

Conclusions:

  • The derived analytical solution enables the precise design of inversion pulses with constant adiabaticity.
  • These novel pulses offer sharp inversion selectivity, beneficial for various magnetic resonance applications.
  • The findings have potential applications in Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR), and Magnetic Resonance Imaging (MRI).