Figure 1 shows the Maxwell-Boltzmann distribution of

**speeds**for a certain gas at a certain temperature, such as nitrogen at 298 K. The**speed**at the top of the curve is called the**most probable speed**because the largest number of molecules have that**speed**.What is r in root mean square velocity?

It is defined as the

**square root**of the**average velocity**-squared of the molecules in a gas. It is given by the formula. where v**is the**_{rms}**root mean square**of the**speed**in meters per second, M_{m}is the molar mass of the gas in kilograms per mole,**R**is the molar gas constant, and T is the temperature in kelvins.1

## What is the average velocity?

The

**average**speed of an object is defined as the distance traveled divided by the time elapsed.**Velocity**is a vector quantity, and**average velocity**can be defined as the displacement divided by the time.2

## What is RMS velocity in vibration?

In contrast to the peak

**velocity**amplitude, the**root-mean-square velocity**amplitude of a vibrating machine tells us the**vibration**energy in the machine. The higher the**vibration**energy, the higher the**root-mean-square velocity**amplitude. The term '**root-mean-square**' is often shortened to '**rms**'.3

## What are the units of the root mean square velocity?

It's called a 'root mean square' and technically, it is a speed, not a velocity. However, in chemistry, we ignore the distinction between speed and velocity and use velocity. Remember that kg m

^{2}s^{-}^{2}is called a**Joule**and that the unit on R is usually written J/K mol.4

## What does it mean that R is a universal constant?

The

**gas constant**, also known as the**universal**molar**gas constant**, is a physical**constant**that appears in an equation defining the behavior of a**gas**under theoretically**ideal**conditions. The**gas constant**is, by convention, symbolized R.5

## How do you find the root mean square?

**Square**each

**value**, add up the squares (which are all positive) and divide by the number of samples to find the average

**square**or

**mean square**. Then take the

**square root**of that. This is the '

**root mean square**' (

**rms**) average

**value**.

6

## What is Maxwell Boltzmann classical statistics?

In

**statistical**mechanics,**Maxwell**–**Boltzmann statistics**describes the average**distribution**of non-interacting material particles over various energy states in thermal equilibrium, and is applicable when the temperature is high enough or the particle density is low enough to render quantum effects negligible.7

## How does the speed distribution of gas particles vary with mass of the gas particles?

The average kinetic energy of a

**gas particle**is directly proportional to the temperature. An increase in temperature increases the**speed**in which the**gas molecules**move. All**gases**at a given temperature have the same average kinetic energy. Lighter**gas molecules**move faster than heavier**molecules**.8

## How does the average kinetic energy depend on temperature?

The last postulate of the

**kinetic**molecular theory states that the**average kinetic energy**of a gas particle**depends**only on the**temperature**of the gas. Thus, the**average kinetic energy**of the gas particles increases as the gas becomes warmer.9

## Who are Maxwell and Boltzmann?

In physics (in particular in statistical mechanics), the

**Maxwell**–**Boltzmann**distribution is a particular probability distribution named after James Clerk**Maxwell**and Ludwig**Boltzmann**.10

## What is the Boltzmann equation?

In statistical mechanics,

**Boltzmann's equation**is a probability**equation**relating the entropy S of an ideal gas to the quantity W, the number of real microstates corresponding to the gas' macrostate: (1) where k_{B}is the**Boltzmann**constant (also written as simply k) and equal to 1.38065 × 10^{−}^{23}J/K.11

## What is the Boltzmann distribution?

In statistical mechanics and mathematics, a

**Boltzmann distribution**(also called Gibbs**distribution**) is a probability**distribution**, probability measure, or frequency**distribution**of particles in a system over various possible states.12

## What is written on Boltzmann tombstone?

**Boltzmann**is buried in the Central Cemetery in Vienna. The equation , where S is entropy, k is

**Boltzmann's**constant, stands for the natural logarithm, and W is the number of possible "states" of a system is

**written on Boltzmann's tombstone**, although Planck was actually the first to

**write**down the equation in this form.

13

## What is the Boltzmann machine?

A

**Boltzmann machine**(also called stochastic Hopfield network with hidden units) is a type of stochastic recurrent neural network (and Markov random field).**Boltzmann machines**can be seen as the stochastic, generative counterpart of Hopfield nets.14

## What are Rbms?

A restricted Boltzmann machine (RBM) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs.

15

## What is the Hopfield network?

A

**Hopfield network**is a form of recurrent artificial neural**network**popularized by John**Hopfield**in 1982, but described earlier by Little in 1974.**Hopfield**nets serve as content-addressable ("associative") memory systems with binary threshold nodes.**Hopfield networks**also provide a**model**for understanding human memory.16

## What is meant by pruning in networking?

**Pruning**is the process of deleting irrelevant parts of a belief

**network**before invoking inference. Consider the

**network**in Figure 9(a) for an example, where is an evidence variable and is a query variable. One can

**prune**node from the

**network**, leading to the

**network**in Figure 9(b).

17

## What is Adaptive Resonance Theory?

**Adaptive resonance theory**(ART) is a

**theory**developed by Stephen Grossberg and Gail Carpenter on aspects of how the brain processes information. It describes a number of neural network models which use supervised and unsupervised learning methods, and address problems such as pattern recognition and prediction.

18

## What is backpropagation algorithm in neural network?

**Backpropagation**is a method used in artificial

**neural networks**to calculate a gradient that is needed in the calculation of the weights to be used in the

**network**. It is closely related to the Gauss–Newton

**algorithm**, and is part of continuing research in

**neural backpropagation**.