Question

If a molecule having N atoms has K number
of constraints, how many degree of freedom
does gas possess.​

Answer 1

Answer:

In physics and chemistry, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all states of a system is known as the system's phase space, and the degrees of freedom of the system are the dimensions of the phase space.

The location of a particle in three-dimensional space requires three position coordinates. Similarly, the direction and speed at which a particle moves can be described in terms of three velocity components, each in reference to the three dimensions of space. If the time evolution of the system is deterministic, where the state at one instant uniquely determines its past and future position and velocity as a function of time, such a system has six degrees of freedom.[citation needed] If the motion of the particle is constrained to a lower number of dimensions – for example, the particle must move along a wire or on a fixed surface – then the system has fewer than six degrees of freedom. On the other hand, a system with an extended object that can rotate or vibrate can have more than six degrees of freedom.

Answer 2

Number of degree of freedom is  $N_f=3N-K$ .

Given :

Total number of atoms , N .

Number of constraints , $N_c=K$

We need to find how many degree of freedom  does gas possess.​

We know , number of degree of freedom is given as :

$N_f=3N-N_c$

Putting all value in above equation we get :

$N_f=3N-K$

Hence , this is the required solution .

Learn More :

Degree of freedom

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