# NCERT Physics Class 11 – Chapter 10 Mechanical Properties of Fluids Part 5

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## SA

**Question 20:**

The surface tension and vapour pressure of water at and , respectively. What is the radius of the smallest spherical water droplet which can form without evaporating at ?

**Answer:**

## LA

**Question 21:**

(a) Pressure decreases as one ascends the atmosphere. If the density of air is , what is the change in pressure over a differential height dh?

(b) Considering the pressure p to be proportional to the density, find the pressure p at a height h if the pressure on the surface of the earth is .

(c) If and , at what height will the pressure drop to the value at the surface of the earth?

(d) This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.

**Answer:**

(a) Consider a horizontal parcel of air with cross section A and height dh. Let the pressure on the top surface and bottom surface be and . If the parcel is in equilibrium, then the net upward force must be balanced by the weight.

(b) Let the density of air on the earth’s surface be then

(c)

(d) The assumption is valid only for the isothermal case which is only valid for small distances

**Question 22:**

Surface tension is exhibited by liquids due to force of attraction between molecules of the liquid. The surface tension decreases with increase in temperature and vanishes at boiling point. Given that the latent heat of vaporisation for water the mechanical equivalent of heat density of water Avagadro’s No and the molecular weight of water

(a) Estimate the energy required for one molecule of water to evaporate.

(b) Show that the inter–molecular distance for water is and find its value.

(c) of water in the vapor state at occupies. Estimate the intermolecular distance at boiling point, in the vapour state.

(d) During vaporisation a molecule overcomes a force F, assumed constant, to go from an inter-molecular distance d to ′. Estimate the value of F.

(e) Calculate , which is a measure of the surface tension.

**Answer:**

(a) of water requires

of water requires

Since there are molecules in of water the energy required for molecule to evaporate is

(b) Consider the water molecules to be points at a distance d from each other.

Thus, the volume around one molecule is

The volume around one molecule is

(c) 1 kg of vapour occupies

∴ 1 molecule occupies

If is the inter molecular distance, then

(d)

(e)

**Question 23:**

A hot air balloon is a sphere of radius . The air inside is at a temperature of . How large a mass can the balloon lift when the outside temperature is ?

**Answer:**

Let the pressure inside the balloon be and the outside pressure be

Considering the air to be an ideal gas

where V is the volume of the air inside the balloon, is the number of moles inside and is the temperature inside, and where V is the volume of the air displaced and no is the number of moles displaced and is the temperature outside.

where is the mass of air inside and is the molar mass of air and where is the mass of air outside that has been displaced. If is the load it can raise, then

Air is

Molar mass of air