Behaviour Of Real Gases MCQ Quiz - Objective Question with Answer for Behaviour Of Real Gases - Download Free PDF

CONCEPT:

Spherical Shape of Rain Water Droplet

• The spherical shape of rain water droplets is primarily due to surface tension.
• Surface tension is a physical phenomenon where the surface of a liquid tends to contract and acquire the least surface area possible, leading to the formation of a spherical shape.

EXPLANATION:

• Surface tension acts at the interface between the water and air, pulling the molecules at the surface inward and minimizing the surface area.
• This inward force causes the droplet to adopt a shape with the smallest possible surface area, which is a sphere.
• Other forces such as gravity can distort this shape, but for small droplets, surface tension dominates and they remain nearly spherical.

Therefore, the correct answer is Surface tension.

CONCEPT:

Effect of Temperature on Viscosity

• Viscosity of Liquids:
  • Viscosity is a measure of a liquid's resistance to flow.
  • As temperature increases, the cohesive forces within the liquid decrease, resulting in a decrease in viscosity.
• Viscosity of Gases:
  • Viscosity is a measure of a gas's resistance to flow.
  • As temperature increases, the kinetic energy of gas molecules increases, causing more frequent and more forceful collisions between molecules.
  • This increased molecular motion and interaction result in an increase in viscosity.

EXPLANATION:

• For liquids: Increased temperature → Decreased cohesive forces → Decreased viscosity
• For gases: Increased temperature → Increased molecular motion → Increased viscosity

Therefore, with a rise in temperature In case of liquids, decreases and in case of gases, increases.

CONCEPT:

Capillary Rise and Contact Angle

\(h =\frac {2Tcosθ}{rρg}\)

• The height (h) of the liquid column in a capillary tube is related to the surface tension (T) and the contact angle (θ) by the formula:
• Here:
  • h = height of liquid column
  • T = surface tension of the liquid
  • θ = contact angle
  • r = radius of the capillary
  • ρ = density of the liquid
  • g = acceleration due to gravity
• This equation assumes that the liquid is in static equilibrium.

EXPLANATION:

Given :

• \(r = 0.2 \ mm = 0.02 \ cm\)
• \(T = 40 \ dyne/cm \ [1\ dyne= 1\ g.cm/s^2]\)
• \(h = 1.5 \ cm\)
• \(ρ = 1 \ g/cm3 \ (assuming \ the \ liquid \ is \ water)\)
• \(g = 980 \ cm/s2\)

Now-

 \(cosθ = \frac {h × r × ρ × g}{2T}\)

Substitute the values:

\(cosθ = \frac {1.5 × 0.02 × 1 × 980}{2 × 40}\)

\(cosθ= \frac {29.4}{80}\)

\(cosθ= 0.3675\)

\(θ = cos^{-1}(0.3675)\)

Calculate θ using the inverse cosine function:

\(θ ≈ 68.4°\)

Therefore, the contact angle of the liquid with the tube is approximately 68.4°.

(A) As temperature increases, the peak (maxima) of a curve is shifted towards the right side.
This implies that the fraction of the molecules with given kinetic energy increases with an increase in the temperature.
Hence, option A is correct.

(B) As temperature increases, the most probable velocity of molecules increases but the fraction of molecules of maximum velocity decreases.
This is because with an increase in temperature the kinetic energy increases.
Hence, option B is correct.

(C) The area under the curve at all the temperatures is the same because it represents the number of gaseous molecules.
At different temperatures, the total number of the gas molecules remains the same.
Hence, option C is correct.

(D) The fractions of molecules have different velocities are different at a given temperature.
They have different kinetic energies.
Hence, option D is correct.

CONCEPT:

Capillary Rise Formula

• The height of the liquid column in a capillary tube due to surface tension is given by the formula:

  h = (2Tcosθ) / (ρgr)

• Where:
  • h: Height of the liquid column (in cm)
  • T: Surface tension of the liquid (in dyne/cm)
  • θ: Contact angle (assume θ = 0° for complete wetting, so cosθ = 1)
  • ρ: Density difference between liquid and air (in g/cm³)
  • g: Gravitational acceleration constant (in cm/s²)
  • r: Radius of the capillary tube (in cm)
• Rearranging the formula to find the radius:

  r = (2Tcosθ) / (hρg)

EXPLANATION:

• Given values:
  • h = 1.0 cm
  • T = 73.2 dyne/cm
  • cosθ = 1 (since θ = 0°)
  • ρ = 0.996 g/cm³
  • g = 980 cm/s²

Substitute the values into the formula:

r = (2 × 73.2 × 1) / (1.0 × 0.996 × 980)

r = 146.4 / 975.84

r = 0.149 cm

r ≈ 0.15 cm

Therefore, the internal radius of the capillary is approximately 0.15 cm.

Concept :

• Food is cooked faster in a pressure cooker because due to high pressure the boiling point of water is raised.
• A pressure cooker works on the principle that with rising pressure the boiling point of water increases.
• Due to the high-pressure boiling point of water rises from 100o C to around 120o C.
• So, the steam also becomes hotter and is also trapped inside the cooker resulting in faster cooking of food.
• When cooked in open vessels the hot air escapes.
• But in the pressure cooker moisture surrounding the food itself reaches higher temperatures than it would without the pressure which speeds the cooking.
• So, the cooking speed is increased nearly four times. 

Hence we can conclude that the beans are cooked faster in pressure cooker because boiling point increase with increasing pressure.

The correct answer is It depends on the room temperature.

Key Points

• The boiling point of a liquid depends on: 
  • the temperature, not the room temperature.
  • the atmospheric pressure,
  • It depends on the nature and purity of the liquid.
  • the vapor pressure of the liquid. 
• The normal boiling point is the temperature at which the vapor pressure is equal to the standard sea-level atmospheric pressure, at sea level, water boils at 100° C (212° F).

The rate of evaporation depends on temperature, the presence of wind, the humidity of the surrounding, and the surface area of the liquid exposed to the atmosphere. It doesn't depend on the mass of the liquid.

• The larger the surface area, the more would be the rate of evaporation.
• The higher the humidity, the slower would be the rate of evaporation.
• The higher the presence of wind, the faster would be the rate of evaporation.
• The higher the temperature, the faster would be the rate of evaporation.

CONCEPT:

Vander-Waals equation

• The equation is basically a modified version of the Ideal Gas Law which states that gases consist of point masses that undergo perfectly elastic collisions.
  • However, this law fails to explain the behavior of real gases. Therefore, the Van der Waals equation was devised and it helps us define the physical state of a real gas.
  • Van der Waals equation is an equation relating the relationship between the pressure, volume, temperature, and amount of real gases. For a real gas containing ‘n’ moles, the equation is written as,

​\(\Rightarrow \left ( P+\frac{an^{2}}{V^{2}} \right )\left ( V-nb \right )=nRT\)     -----(1)

Where P, V, T, n are the pressure, volume, temperature, and moles of the gas and  ‘a’ and ‘b’ constants specific to each gas

Rearranging the above equation, we get 

\(P = \dfrac{nRT}{V-nb} - \dfrac{n^2 a}{V^2}\)

The correct answer is option 2) The molecules in a liquid are arranged in a regular pattern.

Concept:

Matter - It is concerned with the composition, structure, and properties of matter and the phenomenon which occurs when different kinds of matter undergo changes. 

• They can be classified into different categories based on the physical properties exhibited by them and the states in which they exist; these are called states of matter. 
• The basic three states of matter are - solid, liquid, and gas.

Explanation:

Solid - In this, particles are tightly or closely packed in a regular arrangement.

• There is less gap between the particles and hence it is tough to compress them.
• Due to its rigid nature, particles in a solid can only vibrate about their mean position and cannot move freely.
• It has a fixed shape and volume.
• Examples - solid, ice, sugar, rock, wood, etc.

Liquid - In this, the molecules are closely packed because of weak intermolecular forces but in an irregular pattern. 

• They take the shape of the container in which they are kept.
• Liquids have fixed volume but no fixed shape.
• Examples - water, milk, blood, coffee, etc.

Gas - In this, particles are far apart from each other.

• The Force of attraction between the particles is negligible, so they can move freely.
• Gases have neither a fixed volume nor a fixed shape.
• Examples - Air, helium, nitrogen, oxygen, carbon dioxide, etc.

Therefore, the statement that is not true is- the molecules in a liquid are arranged in a regular pattern.

The correct answer is by applying pressure and reducing temperature.

Key Points

• Gas liquefaction involves cooling gas to a temperature below its boiling point so that it can be stored and transported in its liquid phase.
• The gases can be converted into liquids by bringing its particles closer.
  • So, atmospheric gases can be liquefied either by decreasing temperature or by increasing pressure, sometimes a mix of both.

Additional Information

• As the temperature increases, the volume of the gas also increases due to an expansion of gas molecules.
• As the temperature decreases, the volume of the gas also decreases due to the contraction of gas molecules.

CONCEPT:

Spherical Shape of Rain Water Droplet

• The spherical shape of rain water droplets is primarily due to surface tension.
• Surface tension is a physical phenomenon where the surface of a liquid tends to contract and acquire the least surface area possible, leading to the formation of a spherical shape.

EXPLANATION:

• Surface tension acts at the interface between the water and air, pulling the molecules at the surface inward and minimizing the surface area.
• This inward force causes the droplet to adopt a shape with the smallest possible surface area, which is a sphere.
• Other forces such as gravity can distort this shape, but for small droplets, surface tension dominates and they remain nearly spherical.

Therefore, the correct answer is Surface tension.

Concept :

• Food is cooked faster in a pressure cooker because due to high pressure the boiling point of water is raised.
• A pressure cooker works on the principle that with rising pressure the boiling point of water increases.
• Due to the high-pressure boiling point of water rises from 100o C to around 120o C.
• So, the steam also becomes hotter and is also trapped inside the cooker resulting in faster cooking of food.
• When cooked in open vessels the hot air escapes.
• But in the pressure cooker moisture surrounding the food itself reaches higher temperatures than it would without the pressure which speeds the cooking.
• So, the cooking speed is increased nearly four times. 

Hence we can conclude that the beans are cooked faster in pressure cooker because boiling point increase with increasing pressure.

The correct answer is It depends on the room temperature.

Key Points

• The boiling point of a liquid depends on: 
  • the temperature, not the room temperature.
  • the atmospheric pressure,
  • It depends on the nature and purity of the liquid.
  • the vapor pressure of the liquid. 
• The normal boiling point is the temperature at which the vapor pressure is equal to the standard sea-level atmospheric pressure, at sea level, water boils at 100° C (212° F).

The rate of evaporation depends on temperature, the presence of wind, the humidity of the surrounding, and the surface area of the liquid exposed to the atmosphere. It doesn't depend on the mass of the liquid.

• The larger the surface area, the more would be the rate of evaporation.
• The higher the humidity, the slower would be the rate of evaporation.
• The higher the presence of wind, the faster would be the rate of evaporation.
• The higher the temperature, the faster would be the rate of evaporation.