NCERT solution Class 11 kinetic theory

NCERT Solutions

Class 11 Physics

Kinetic Theory

NCERT Questions

Q. 12.1
Q. 12.2
Q. 12.3
Q. 12.4
Q. 12.5
Q. 12.6
Q. 12.7
Q. 12.8
Q. 12.9
Q. 12.10

Q. 12.4

An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C Estimate the mass of oxygen taken out of the cylinder (R = 8.31 J mol^–1 K^–1, molecular mass of O₂ = 32 u).

Given:

Volume of oxygen, V₁ = 30 litres = 30 × 10^–3 m³

Gauge pressure, P₁ = 15 atm = 15 × 1.013 × 10⁵ Pa

Temperature, T₁ = 27°C = 300 K

Universal gas constant, R = 8.314 J mole^–1 K^–1

Let the initial number of moles of oxygen gas in the cylinder be n₁.

The gas equation is given as:

P₁V₁ = n₁RT₁

n₁ = = = 18.276

But, n₁= Where, m₁ = Initial mass of oxygen

M = Molecular mass of oxygen = 32 g

m₁ = (n₁M) = 18.276 × 32 = 584.84 g

After some oxygen is withdrawn from the cylinder, the pressure and temperature reduces.

Volume, V₂ = 30 litres = (30 × 10^–3) m³

Gauge pressure, P₂ = 11 atm = (11 × 1.013 × 10⁵) Pa

Temperature, T₂ = 17°C = 290 K

Let n₂ be the number of moles of oxygen left in the cylinder.

The gas equation is given as:

P₂V₂ = n₂RT₂

n₂=

= 13.86

But, n₂ = Where, m₂ is the mass of oxygen remaining in the cylinder

m₂ = (n₂M) = 13.86 × 32

= 453.1 g

The mass of oxygen taken out of the cylinder is given by the relation:Initial mass of oxygen in the cylinder – Final mass of oxygen in the cylinder

= (m₁ – m₂) = 584.84 g – 453.1 g = 131.74 g = 0.131 kg

Therefore, 0.131 kg of oxygen is taken out of the cylinder.

Video solution:

Kinetic Theory Class 11 Physics NCERT Chapter 12 NCERT Solutions

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