velocity

Examples of velocity in the following topics:

• Root-Mean-Square Speed

  • We use velocity to describe the movement of gas particles, thereby taking into account both speed and direction.
  • Although the velocity of gaseous particles is constantly changing, the distribution of velocities does not change.
  • Particles moving in opposite directions have velocities of opposite signs.
  • By squaring the velocities and taking the square root, we overcome the "directional" component of velocity and simultaneously acquire the particles' average velocity.
  • Recall the mathematical formulation of the root-mean-square velocity for a gas.

• Distribution of Molecular Speeds and Collision Frequency

  • (Velocity is a vector quantity, equal to the speed and direction of a particle) To properly assess the average velocity, average the squares of the velocities and take the square root of that value.
  • This is known as the root-mean-square (RMS) velocity, and it is represented as follows:
  • If we assume that all velocity states are equally probable, higher velocity states are favorable because there are greater in quantity.
  • Using the above logic, we can hypothesize the velocity distribution for a given group of particles by plotting the number of molecules whose velocities fall within a series of narrow ranges.
  • Velocity distributions are dependent on the temperature and mass of the particles.

• Viscosity

  • This is called laminar flow (also known as streamlined flow), and the velocity of the fluid's flow varies from close to zero near the pipe's boundaries to its greatest in the center.
  • The force required to move the plate at a constant speed is directly proportional to the area of the plate and to the fluid's velocity gradient as we move at a greater perpendicular distance from the plate (meaning how fast the velocity of the layers is changing as we move away from the plate).
  • Velocity of a fluid's layers, or lamina, during smooth flow.
  • The velocity is greatest at the center of the tube.
  • Note the magnitude of the velocity vectors for layers increasingly away from the moving plate.

• Indeterminacy and Probability Distribution Maps

  • According to classical physics, particles move in a very specific trajectory that is completely determined by the particle's velocity, position, and the sum of any forces acting on it.
  • A bullet propelled from a gun at a consistent velocity under identical conditions will always follow the same trajectory and hit the same target.
  • Recall from the uncertainty principle that we cannot simultaneously know an electron's position and velocity—therefore we are unable to determine its trajectory.
  • Since either its present position or velocity is unknown, we cannot know where it will be with any certainty after a known time interval.

• Molecularity

  • If a chemical reaction proceeds by more than one step or stage, its overall velocity or rate is limited by the slowest step, the rate-determining step.

• Properties of Waves and Light

  • For each medium, there is a characteristic velocity at which the disturbance travels.
  • The relation between the wavelength λ (Greek lambda) and frequency of a wave ν (Greek nu) is determined by the propagation velocity v, such that
  • When utilizing these equations to determine wavelength, frequency, or velocity by manipulation of the equation, it is important to note that wavelengths are expressed in units of length, such as meters, centimeters, nanometers, etc; and frequency is typically expressed as megahertz or hertz (s–1).
  • What is the wavelength of the musical note A = 440 hz when it is propagated through air in which the velocity of sound is 343 m s–1?

• Introduction to Chemical Reactivity

  • Catalysts are substances that accelerate the rate ( velocity ) of a chemical reaction without themselves being consumed or appearing as part of the reaction product.

• Gas Diffusion and Effusion

  • The gases' effusion rate is directly proportional to the average velocity at which they move; a gas is more likely to pass through an orifice if its particles are moving at faster speeds.
  • The rate of effusion is determined by the number of molecules that diffuse through the hole in a unit of time, and therefore by the average molecular velocity of the gas molecules.

• Hydrogenation

  • Catalysts are substances that changes the rate (velocity) of a chemical reaction without being consumed or appearing as part of the product.

• Microstates and Entropy

  • In contrast to the macrostate, which characterizes plainly observable average quantities (temperature, for example), a microstate specifies all molecular details about the system, including the position and velocity of every molecule.