# MHT-CET Physics Crash Course “Pressure Exerted by Gas” Class 12

## “Pressure Exerted by Gas” MHT-CET Class 12 Physics Crash Course | Chapter Kinetic theory of Gases and Radiation

In this session G.S. Khairnar discussed the theory and MCQ’s of “Pressure Exerted by Gas”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.

### Pressure Exerted by Gas:-

Dear students in previous article we have learnt about the behaviour of gas molecules on the basis of kinetic theory. The gas molecules are always in state of random motion, due to this they consistently collides on neighbouring molecules and on the wall of vessels. This imparts momentum on the wall of vessel and exerts the pressure.

In this article we are going to find the derivation of pressure exerted by gas molecules filled in vessel.

Let’s derive an expression for the pressure due to gas….!

Consider a perfect gas is filled in cubical vessel of side ‘l’ as shown below, By assumptions of kinetic theory of gases, the gas molecules are constantly moving in all possible direction with all possible velocities. Therefore they possess momentum thus exerts pressure on wall of container.

N= number of molecules of gas.

m=mass of each molecule of gas.

M=Nm= Total mass of gas.

A= l2= Area of face of cube.

V= l3= Volume of cube.

ρ=M/V= Density of gas.

Imagine that the gas molecules are moving in XYZ co-ordinate axes with different velocities C1, C2…CN. Let u1, v1, w1 are the components of velocity C1 along X, Y and Z axes respectively. Similarly velocities of remaining molecules can be given as, Consider a gas molecule of mass m is moving along X axis with velocity u1.Then its initial momentum is given as,

initial momentum=mu1

The gas molecule will collide on wall of container and moves in opposite direction with velocity – u1, therefore the final momentum of gas molecule is,

final momentum=-mu1

∴ The Change in momentum of gas molecule per unit collision

= Final momentum- Initial momentum.

= -mu1– mu1

= -2 mu1

∴ The Change in momentum of gas molecule per unit collision =|-2 mu1 |

∆P=2 mu1 ……….(1)

The distance travelled by gas molecule during this collision is ‘2l’ with velocity

∴ Time taken by molecule during this collision, Then according to Newton’s second law, force exerted by this molecule is given as, Similarly, forces due other molecules moving towards X- axis are, By definition, pressure exerted by molecules along X-axis is given by, Some important points to note…..!

1. Pressure of gas increases with increase in density of gas.
2. Pressure of gas is directly proportional to square of rms speed of gas molecules.
3. By kinetic theory, the pressure exerted by gas molecules is, ### Let’s solve some MCQ’s…!

Q.1) The pressure exerted by gas filled in vessel is given as by formula… Q.2) According to kinetic theory of gases, during collisions of gas molecules the kinetic energy of molecules…

a) increases

b) decreases

c) remains same

d) can not predicted

c) remains same

Q.3) Oxygen is filled in two different vessels has rms speeds in ration 2:3. Ratio of pressure exerted by oxygen in vessels is…

a) 3:2

b) 2:3

c) 9:4

d) 4:9

d) 4:9 Q.4) A gas of density of 0.64 kg/m3 at NTP exerts pressure of 16 × 104 Pa, the rms speed of gas is… Q.5) RMS speed of gas at 300 K is 25 m/s, RMS speed of the gas at 2700 K is…

a) 25 m/s

b) 25 cm/s

c) 75 m/s

d) 75 cm/s

c) 75 m/s Q.6) According to kinetic theory of gas, pressure exerted by the gas is….

a) directly propotional to number of molecules

b) directly propotional to mass of each molecule

c) inversly proportinal to volume of vessel

d) all statement from (a) to (c)are correct

d) all statement from (a) to (c)are correct

### ♦जिल्हा नुसार जाहिराती ♦

अहमदनगर अकोला अमरावती औरंगाबाद भंडारा बुलढाणा
चंद्रपुर धुले गढ़चिरौली गोंदिया हिंगोली जलगांव
जालना कोल्हापुर लातूर मुंबई नागपुर नांदेड़
नंदुरबार नाशिक उस्मानाबाद पालघर परभानी पुणे
रायगढ़ रत्नागिरि सांगली सातारा सिंधुदुर्ग सोलापुर
ठाणे वर्धा वाशिम यवतमाल बीड

### ♦शिक्षणानुसार जाहिराती ♦

७ वी (7th) दहावी (SSC) बारावी (HSC) डिप्लोमा आय.टी.आय पदवी
पदव्युत्तर शिक्षण बी.एड एम.एड एल.एल.बी / एल.एल.एम बीएससी एमबीए
बीसीए एमसीए बी.कॉम एम.कॉम GNM/ANM एमएससी
बी.फार्म एम.फार्म बी.ई एम.ई BAMS/BHMS एम.बी.बी.एस / एम.डी
बी.टेक एम.टेक MS-CIT