# Topic: Kinetic Theory (Test 1)

Topic: Kinetic Theory
Q.1
Kinetic theory explains the behavior
A. of liquids based on the idea that the liquids consist of rapidly moving atoms or molecules
B. of solids based on the idea that the solid consists of rapidly vibrating atoms or molecules
C. of solids and liquids based on the idea that they gas consist of rapidly vibrating atoms or molecules
D. of gases based on the idea that the gas consists of rapidly moving atoms or molecules
Explaination / Solution:

The theory for ideal gases makes the following assumptions 1. Gases consist of particles in constant, random motion. They continue in a straight line until they collide with something—usually each other or the walls of their container. 2. Particles are point masses with no volume. The particles are so small compared to the space between them, that we do not consider their size in ideal gases. 3. No molecular forces are at work. This means that there is no attraction or repulsion between the particles. 4. Gas pressure is due to the molecules colliding with the walls of the container. All of these collisions are perfectly elastic, meaning that there is no change in energy of either the particles or the wall upon collision. No energy is lost or gained from collisions. 5. The time it takes to collide is negligible compared with the time between collisions. 6. The kinetic energy of a gas is a measure of its Kelvin temperature. Individual gas molecules have different speeds, but the temperature and kinetic energy of the gas refer to the average of these speeds. 7. The average kinetic energy of a gas particle is directly proportional to the temperature. An increase in temperature increases the speed in which the gas molecules move. 8. All gases at a given temperature have the same average kinetic energy. 9. Lighter gas molecules move faster than heavier molecules.

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Q.2
In which case are the atoms relatively rigidly fixed?
A. liquids and gases
B. gases
C. solids
D. liquids
Explaination / Solution:

Atoms in a gas are well separated with no regular arrangement. Atoms vibrate and move freely at high speeds Atoms in a liquid are close together with no regular arrangement. Atoms vibrate, move about, and slide past each other. Atoms in a solid are tightly packed, usually in a regular pattern. Atoms vibrate (jiggle) but generally do not move from place to place.

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Q.3

If there are n number of molecules per unit volume and m is the mass of each ,  is the x-component of velocity, pressure can be written as

A. P=mv2x¯¯¯¯¯
B. P=nmv2x¯¯¯¯¯
C. P=nv2x¯¯¯¯¯
D. P=2nmv2x¯¯¯¯¯
Explaination / Solution:

Pressure is due to collision of molecule with the wall of container.

Collision by moleculeto the wall of conntainer assumed to be perfectly elastic.

By the principle of conservation of momentum, the momentum imparted to the wall in the collision = 2mvx

the number of molecules hitting the wall in time  =

n  = no. of molecule per unit volume

A = Area of container

The total momentum transferred to the wall by these molecules in   time =

Pressure P = F/A = rate of momentum transfer per unit area

all molecules in a gas do not have the same velocity; there is a distribution in velocities. The  above equation therefore, stands for pressure due to the group of molecules with speed vx   in  the x-direction and n stands for the number density of that group of molecules. The total pressurer due to  all  groups

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Q.4
The molar specific heat at constant volume,  for monatomic gases is
A.
R
B. 32R
C. R
D. R
Explaination / Solution:

for monatomic gases f = 3

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Q.5

Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP : 1 atmospheric pressure, 0 C). The value of Molar volume is

A. 22.4 liters
B. 24.4 liters
C. 20.4 liters
D. 23.7 liters
Explaination / Solution:

PV=nRT

V=nRTP=1×8.31×2731.01×105=0.02224m3=22.4lit

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Q.6
Estimate the average thermal energy of a helium atom at the temperature on the surface of the Sun (6000 K)
A. 1.35   J
B. 1.28   J
C. 1.20   J
D. 1.24×1019J
Explaination / Solution:

k = boltzman constant

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Q.7
In constructing a large mobile, an artist hangs an aluminum sphere of mass 6.0 kg from a vertical steel wire 0.50 m long and 2.5   in cross-sectional area. On the bottom of the sphere he attaches a similar steel wire, from which he hangs a brass cube of mass 10.0 kg. Compute the tensile strain.

A. 3.1   upper, 2.0   lower
B. 3.2   upper, 2.3   lower
C. 3.3   upper, 2.4   lower
D. 3.4   upper, 2.5   lower
Explaination / Solution:
No Explaination.

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Q.8

Nine particles have speeds of 5.00, 8.00, 12.0, 12.0, 12.0, 14.0, 14.0, 17.0, and 20.0 m/s. What is the rms speed?

A. 2.52   m
B.
3.16   m

C.
2.25   m

D. 2.25   m
Explaination / Solution:

no. of molecule per unit volume

mean free path

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Q.9
What is the average kinetic energy of the helium atoms in a balloon of diameter 30.0 cm at 20.0C and 1.00 atm?
A. 7.13   J
B. 6.07   J
C. 5.79   J
D. 6.57   J
Explaination / Solution:

K¯=32kT=32×1.38×1023×293=6.07×1021J
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Q.10
One mole of hydrogen gas is heated at constant pressure from 300 K to 420 K. Calculate the energy transferred by heat to the gas
A. 3.66 kJ
B. 3.49 kJ
C. 3.86 kJ
D. 3.26 kJ