Tag: kinetic theory of gases

Quizzes (6) Questions (57)

Questions Related to kinetic theory of gases

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

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

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The mean free path lambda = 1 / (sqrt(2) * pi * d^2 * n). Since n = P / (kT), lambda = kT / (sqrt(2) * pi * d^2 * P). Thus, lambda is directly proportional to temperature T.

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

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

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  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.
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. Have finite volume

  2. Obey Boyle's law

  3. Possess momentum

  4. Collide with one another
Reveal answer Fill a bubble to check yourself
C Correct answer
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.
Multiple choice modelling gases - the kinetic model ideal gases kinetic theory of gases physics

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?
$(\sigma  = 5.67 x10^{-8} Wm^{-2}K^{-4})$.

  1. $120^{o}C$

  2. $63.9^{o}C$

  3. $50.7^{o}C$

  4. $31.4^{o}C$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $I _{sc} = 1353 Wm^{-2}$

Multiple choice physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

A glass capillary tube sealed at both ends is 100cm long. It lies horizontally with the middle 10cm containing mercury. The two ends of the tube which are equal in length contain air at $27 ^ { 0 } \mathrm { C }$ at a pressure of 76cm of Hg. Now the air column at one end of the tube is kept at $0 ^ { 0 } \mathrm { C }$ and the other end is maintained at $127 ^ { \circ } C$. Calculate the pressure of the air column at $0 ^ { \circ } \mathrm { C }$. (Neglect the change in volume of Hg and glass).

  1. $25$ cm of HG

  2. $35$ cm of HG

  3. $55$ cm of HG

  4. $85$ cm of HG
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the ideal gas law PV = nRT, since the amount of gas and the total volume are constant, we relate the pressures and temperatures. The pressure of the gas at 0C (273K) and 127C (400K) must satisfy the condition that the total length of the air columns remains constant (90cm total). Solving the system of equations for the pressure P leads to 35 cm of Hg.

Multiple choice physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

One mole of n ideal monatomic  gas undergoes the following four reversible processes:
Step I: It is first compresses adiabatically from volume $V _1$ to $1m^3$.
Step II: then expanded isothermally to volume $10 m^3$.
Step III: then expanded adiabatically to volume $V _3$.
Step IV: then compressed isothermally to volume $V _1$.
If the efficiency of the above cycle is $3/4$ then V, is

  1. $2 m^3$

  2. $4 m^3$

  3. $6 m^3$

  4. $8 m^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The efficiency of a Carnot-like cycle involving adiabatic and isothermal steps is 1 - (T_cold / T_hot). For an ideal gas, the temperature ratio is related to volume ratios via adiabatic relations (T * V^(gamma-1) = constant). Given efficiency 3/4, the ratio of temperatures is 1/4, which allows solving for V3 in terms of V1.

Multiple choice physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

Solid floating in a liquid . On decreasing the temperature solid sinks into the liquid . If ${ \Upsilon  } _{ l }\quad and\quad { \alpha  } _{ s }$ are volume expansion coefficient of liquid and linear expansion coefficient of solid , then :

  1. ${ \Upsilon } _{ l }\quad <\quad 3{ \alpha } _{ s }$

  2. ${ \Upsilon } _{ l }\quad >\quad 3{ \alpha } _{ s }$

  3. ${ \Upsilon } _{ l }\quad =\quad 3{ \alpha } _{ s }$

  4. ${ \Upsilon } _{ l }\quad =\quad 2{ \alpha } _{ s }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A solid floats if its density is less than the liquid density. If the solid sinks upon cooling, it means the density of the solid increased more than the density of the liquid, or the liquid density decreased relative to the solid. Since volume expansion coefficients are related to density changes, the condition for the solid to sink is that the liquid's volume expansion coefficient is greater than the solid's volume expansion coefficient (3 * alpha).