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Modelling gases - the kinetic model - class-XII

Description: modelling gases - the kinetic model
Number of Questions: 17
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Tags: ideal gases kinetic theory of gases physics
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The gas, which is present the most in air, is___

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. oxygen

  2. nitrogen

  3. carbon dioxide

  4. water vapour

Show answer
Correct Option: B
Explanation:

1) Nitrogen $-78$%

2) Oxygen $-21$%
3) Inert Nobel gases $-0.9$%
4) Several trace gases $-0.1$%
The above list the different number of gases in descending order. As per the list clearly Nitrogen is the gas present in most air.

Heat is associated with 

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. kinetic energy of random motion of molecules

  2. kinetic energy of orderly motion of molecules

  3. total kinetic energy of random and orderly motion of molecules

  4. kinetic energy of random motion in some cases and kinetic energy orderly motion in other.

Show answer
Correct Option: A
Explanation:

Heating up a substance excites the molecules of that substance making  the molecules moves vigorously thus giving velocity to the molecules and we know kinetic energy of a body is by the virtue of its motion.       

The kinetic energy of translation of $20gm$ of oxygen at $47^oC$ is (molecule wt. of oxygen is $32gm/mol $and $R=8.3J/mol/K$)

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. 2490 joules

  2. 2490 ergs

  3. 830 joules

  4. 124.5 joules

Show answer
Correct Option: A

What is an ideal gas?

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. One that consists of molecules

  2. A gas satisfying the assumptions of kinetic theory

  3. A gas having Maxwellian distribution of speed

  4. A gas consisting of massless particles

Show answer
Correct Option: B
Explanation:

An ideal gas is a gas which satisfying the assumptions of the kinetic energy.

Statement 1: The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.
Statement 2: A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. Statement 1 is true, statement 2 is true and statement 2 is correct explanation of statement 1

  2. statement 1 is true, statement 2 is false

  3. Statement 1 is true, Statement 2 is true but Statement 2 is not the correct explanation of Statement 1

  4. Statement 1 is false, Statement 2 is true

Show answer
Correct Option: C

A body at a temperature of ${ 727 }^{ \circ  }C$ and having surface area ${ 5cm }^{ 2 }$ , radiated 300J of energy each minute. The emissivity (Given: boltzmann constant=$ 5.67\times { 10 }^{ -8 }{ Wm }^{ -2 }{ K }^{ -4 }$ is

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. e=0.2

  2. e=0.02

  3. e=0.18

  4. e=0.15

Show answer
Correct Option: A

The average pressure of an ideal gas is  

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. $\rho = (1/3)\, mn \, V^2 _{av}$

  2. $\rho = (1/2)\, mn \, V _{av}$

  3. $\rho = (1/4)\, mn \, V^2 _{av}$

  4. $\rho = (1/3)\, mn \, V _{av}$

Show answer
Correct Option: A

The pressure of air increases by $100mm$ of Hg and the temperature decreases by $1^0C$. The change in the speed of sound in air at STP is

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. $61ms^{-1}$

  2. $61mms^{-1}$

  3. $61 cms^{-1}$

  4. $0.61 cms^{-1}$

Show answer
Correct Option: D

The equation of state of some gases can be expressed as (p+av2)(v−b)=RT Here p is pressure, v is volume , a,b,R are constants. The dimensions of ′a′ are

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. $ML^{-5}T^{-2}$

  2. $ML^{-1} T^{-2}$

  3. $M^o L^3T^o$

  4. $M^B L^oT^o$

Show answer
Correct Option: A
Explanation:

Here $P$ and $a/{ V }^{ 2 }$ are added that means they have same dimensions.

Therefore,
$\left[ { M }^{ 1 }{ L }^{ -1 }{ T }^{ -2 } \right] =\dfrac { a }{ \left[ { M }^{ 0 }{ L }^{ 6 }{ T }^{ 0 } \right]  } $
$a=\dfrac { { M }^{ 1 }{ L }^{ -1 }{ T }^{ -2 } }{ { M }^{ 0 }{ L }^{ 6 }{ T }^{ 0 } } $
$a={ M }^{ 1 }{ L }^{ 5 }{ T }^{ -2 }$

According to kinetic theory of gases,

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. The velocity of molecules decreases for each collision

  2. The pressure exerted by a diatomic gas is proportional to teh mean velocity of the molecule

  3. The K.E of the gas decreases on expansion at constant temperature

  4. The mean translational KE of a diatomic gas increases with increase in absolute temperature

Show answer
Correct Option: D
Explanation:

Options:
(A): One can not say velocity of molecule decreases  in each collision.
(B): The pressure exerted by a diatomic gas is proportional to rms speed, not mean speed.
(C): Since temp is constant, KE will be constant.
(D): Mean translational KE is proportional to temp, hence will increase with increase in absolute temp.

Consider the following statements for air molecules in an air tight container.

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. the average speed of molecules is larger than root mean square speed.

  2. mean free path of molecules is larger than the mean distance between molecules

  3. mean free path of molecules increases with temperature.

  4. the rms speed of nitrogen molecules is smaller

Show answer
Correct Option: C

Gas exerts pressure on the walls of container because the molecules:

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. Are losing their Kinetic Energy

  2. Are getting stuck to the walls

  3. Are transferring their momentum to walls

  4. Are accelerated towards walls

Show answer
Correct Option: C
Explanation:

Pressure is force per unit area

and force is nothing but the rate of change of momentum
When the molecules collide with wall their direction get changed so their momentum get changed and this difference
 in momentum after and before the collision is given to the walls so walls feel a force consequently Pressure.
Energy remains constant because collisions are supposed to be $elastic$
Option C is correct.

solids expand on heating because

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. Kinetic energy of the atoms increases

  2. Total energy of the atoms increases

  3. The potential energy curve is asymmetric atoms

  4. none of these

Show answer
Correct Option: A

Which of the following statements is NOT a correct assumption of the model of an ideal monatomic gas?

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. The atoms are constantly moving.

  2. The collision between atoms create pressure directly on the container of the gas.

  3. The collision between atoms are elastic.

  4. The only significant forces acting on the atoms are those that are applied as a result of collisions.

  5. The volume of each atom can be neglected.

Show answer
Correct Option: B
Explanation:

Pressure is created by the atom of the gas when the collide with the container. during collision the atoms apply force on the container wall. This force per unit area is the pressure of the gas.

When we heat a gas sample from $27^{\circ}$ and $327^{\circ}$, then the initial average kinetic energy of the molecules was $E$. What will be the average kinetic energy after heating?

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. $\sqrt{2}\ E$

  2. $2\ E$

  3. $300\ E$

  4. $327\ E$

Show answer
Correct Option: C

Gases exert pressure on the walls of the container because the gas molecules.

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. Have finite volume

  2. Obey Boyle's law

  3. Possess momentum

  4. Collide with one another

Show answer
Correct Option: C
Explanation:
Pressure exerted by the gas molecules on the walls of container is calculated by the no. of collisions on the wall.
What a collision on the wall do is they apply a force on the wall due to the change in momentum of molecules.
$\Rightarrow$ Pressure $=\dfrac{force}{Area}=\dfrac{dP}{Adt}$
Where $dP$ is change in momentum.
Hence, the answer is Possess momentum.

Solar radiation reaches the earths atmosphere at a rate of $1353 Wm^{-2}$. If 36% of this
radiation is reflected back into space and 18% is absorbed by the earths atmosphere. The
radiant emittance is given by $\sigma T^{4}$
 where $\sigma$ is the Stefan-Boltzmanns constant and T is the
absolute temperature. What maximum temperature would an isolated black body on the
earths surface be expected to attain?
$(\sigma  = 5.67 x10^{-8} Wm^{-2}K^{-4})$.

modelling gases - the kinetic model ideal gases kinetic theory of gases physics

  1. $120^{o}C$

  2. $63.9^{o}C$

  3. $50.7^{o}C$

  4. $31.4^{o}C$

Show answer
Correct Option: C
Explanation:

Of the solar radiation reaching the earths atmosphere
36% is reflected back into space
18% is absorbed by the earths atmosphere
This implies that only 46% reaches the earths surface
If absorbed by a black body, expect that the maximum temperature of this body is given by
where $I _{sc} = 1353 Wm^{-2}$

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