A parallel beam of particles of mass m moving | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Consider a small area $A$ on the wall. The number of particles hitting this area in time $\Delta t$ is equal to the number of particles contained

Vedclass · Accepted Answer

$2\, mn\, v^2 \,\cos^2 	heta$

Vedclass · Answer

(B) Consider a small area $A$ on the wall. The number of particles hitting this area in time $\Delta t$ is equal to the number of particles contained in a cylinder of base area $A$ and length $v \Delta t \cos 	heta$.Volume of this cylinder $= A \cdot v \Delta t \cos 	heta$.Number of particles $N = n \cdot A \cdot v \Delta t \cos 	heta$.The number of particles hitting per unit area per unit time is $N' = \frac{N}{A \Delta t} = nv \cos 	heta$.When a particle of mass $m$ hits the wall elastically at an angle $	heta$ to the normal,its velocity component parallel to the wall remains unchanged,while its velocity component perpendicular to the wall reverses direction.Change in momentum of one particle $= m(v \cos 	heta) - m(-v \cos 	heta) = 2mv \cos 	heta$.Pressure $P$ is the force per unit area,which is equal to the rate of change of momentum per unit area.$P = N' 	imes (	ext{change in momentum of one particle}) = (nv \cos 	heta) 	imes (2mv \cos 	heta) = 2mnv^2 \cos^2 	heta$.

$A$ parallel beam of particles of mass $m$ moving with velocity $v$ impinges on a wall at an angle $\theta$ to its normal. The number of particles per unit volume in the beam is $n$. If the collision of particles with the wall is elastic,then the pressure exerted by this beam on the wall is

Similar Questions

If the average translational kinetic energy of a molecule in a gas is equal to the kinetic energy of an electron accelerating from rest through $10 \,V$, then the temperature of the gas molecule is (Boltzmann constant $= 1.38 \times 10^{-23} \,JK^{-1}$)

The average kinetic energy of a gas molecule can be determined by knowing

Assertion $(A)$: The temperature of a gas is a result of the kinetic energy of its molecules.
Reason $(R)$: Due to kinetic energy,the molecules collide with each other to produce thermal energy.

Internal energy of an ideal gas depends on which factors and does not depend on which factors?

The average kinetic energy of a molecule of a gas is

Vedclass Test Series

Exam Paper Generator

Online Exam Module