# NCERT Class 11 Physics Solutions: Chapter 13 – Kinetic Theory-Part 2

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**Question 13.4:**

An oxygen cylinder of volume has an initial gauge pressure of and a temperature of After some oxygen is withdrawn from the cylinder, the gauge pressure drops to and its temperature drops to . Estimate the mass of oxygen taken out of the cylinder

**Answer:**

Volume of oxygen,

Gauge pressure,

Temperature,

Universal gas constant,

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

The gas equation is given as:

But,

Where, Initial mass of oxygen

Molecular mass of oxygen

After some oxygen is withdrawn from the cylinder, the pressure and temperature reduces.

Volume,

Gauge pressure,

Temperature,

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

The gas equation is given as:

But,

Where,

is the mass of oxygen

Remaining in the cylinder:

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

Therefore, of oxygen is taken out of the cylinder.

**Question 13.5:**

An air bubble of volume rises from the bottom of a lake deep at a temperature of To what volume does it grow when it reaches the surface, which is at a temperature of ?

**Answer:**

Volume of the air bubble,

Bubble rises to height,

Temperature at a depth of

Temperature at the surface of the lake,

The pressure on the surface of the lake:

The pressure at the depth of :

Where is the density of water g is the acceleration due to gravity

We have:

Where, is the volume of the air bubble when it reaches the surface

Therefore, when the air bubble reaches the surface, its volume becomes