Question

the pressure of an ideal gas and its mean ke per unit volume are related by the relation

Answer 1

Hello Dear.

The Pressure of an Ideal Gas and its Kinetic Energy per unit Volume are related by the Formula →

 Pressure = 2/3 of Kinetic Energy per unit volume.
⇒ P = (2/3) × K

______________________

Proof →
 
From the Kinetic theory of the gases,the Pressure P exerted by an Ideal Gas of Density ρ and Velocity of the Molecules of the Gas is given by the Relation →

P = (1/3)ρC²   -----eq(i)

∵ Density = Mass/Volume 
∴ Mass of the Unit Volume of the Gas = ρ × 1
   = ρ 

Now,
We know,
Kinetic Energy = 1/2 × mass × Velocity².
∴ K = 1/2 × ρ × C².   ----eq(ii)


Dividing eq(i) by eq(ii),

We get,

 P/K = [(1/3) × ρ C²] ÷ [(1/2) × ρ C²]
⇒ P = 2/3 × K


Hence Proved.

____________________


Hope it helps.

Answer 2

Answer:-

The Pressure of an Ideal Gas and its Kinetic Energy per unit Volume are related by the Formula →

 Pressure = 2/3 of Kinetic Energy per unit volume.

⇒ P = (2/3) × K

______________________

Proof →

 

From the Kinetic theory of the gases,the Pressure P exerted by an Ideal Gas of Density ρ and Velocity of the Molecules of the Gas is given by the Relation →

P = (1/3)ρC²   -----eq(i)

∵ Density = Mass/Volume 

∴ Mass of the Unit Volume of the Gas = ρ × 1

   = ρ 

Now,

We know,

Kinetic Energy = 1/2 × mass × Velocity².

∴ K = 1/2 × ρ × C².   ----eq(ii)

Dividing eq(i) by eq(ii),

We get,

 P/K = [(1/3) × ρ C²] ÷ [(1/2) × ρ C²]

⇒ P = 2/3 × K

Hence Proved.

____________________

Hope it's help You❤️