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Kinetic Theory Of Gases Test - 5

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Kinetic Theory Of Gases Test - 5

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Question 1
1 / -0

Kinetic theory explains the behavior

A
of liquids based on the idea that the liquids consist of rapidly moving atoms or molecules

B
of gases based on the idea that the gas consists of rapidly moving atoms or molecules

C
of solids based on the idea that the solid consists of rapidly vibrating atoms or molecules

D
of solids and liquids based on the idea that they gas consist of rapidly vibrating atoms or molecules

Solution

Explanation:
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.
Question 2
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The number of degrees of freedom a diatomic molecule is

A
5.0

B
6

C
3

D
5.3

Solution

A diatomic molecule has 5 degrees of freedoms - 3 translational degrees each in one principal axis and 2 rotational degrees of freedom.
Question 3
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Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). The number of molecules

A
is the same in all three vessels

B
is the greatest in the vessel with neon

C
is the greatest in the vessel with chlorine

D
is the greatest in the vessel with uranium hexafluoride

Solution

Explanation:Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules".
Question 4
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A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm². Calculate the elongation of the wire when the mass is at the lowest point of its path.

A
1.339 × 10⁻⁴ m

B
1.439 × 10⁻⁴ m

C
1.879 × 10⁻⁴ m

D
1.239 × 10⁻⁴ m

Solution

Mass, m = 14.5 kg
Length of the steel wire, l = 1.0 m
Angular velocity, ω = 2 rev/s = 2 × 2π rad/s = 12.56 rad/s
Cross-sectional area of the wire, a = 0.065 cm² = 0.065 × 10^-4 m²
Let Δl be the elongation of the wire when the mass is at the lowest point of its path.
When the mass is placed at the position of the vertical circle, the total force on the mass is:
F = mg + mlω²
= 14.5 × 9.8 + 14.5 × 1 × (12.56)²
= 2429.53 N
Young’s modulus = Strss / Strain
Y = (F/A) / (∆l/l)
∴ ∆l = Fl / AY
Young’s modulus for steel = 2 × 10¹¹ Pa
∆l = 2429.53 × 1 / (0.065 × 10^-4 × 2 × 10¹¹) = 1.87 × 10^-3 m
Hence, the elongation of the wire is 1.87 × 10^–3 m
Hence 1.87 × 10^–3 m
Question 5
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One mole of an ideal monatomic gas is at an initial temperature of 300 K. The gas undergoes an isovolumetric process, acquiring 500 J of energy by heat. It then undergoes an isobaric process, losing this same amount of energy by heat. Determine the new temperature of the gas

A
333 K

B
316 K

C
343 K

D
301 K

Solution

Explanation:
for monoatomic gas C_V= 1.5R, C_P = 2.5R
At const volume,
Q = 500 J
Q=nCVΔT
500=1×1.5×8.31(T₁−300)
T₁=340K
At const pressure Q = 500 J
Q=nCPΔT
500=1×2.5×8.31(340−T₂)
T₂=316K
Question 6
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Kinetic theory

A
correctly explains specific heat capacities of many gases

B
correctly explains specific heat capacities of super cooled liquids

C
correctly explains specific heat capacities of many solids

D
correctly explains specific heat capacities of many liquids

Solution

Explanation:The kinetic theory describes a gas as a large number of submicroscopic particles (atoms or molecules), all of which are in constant rapid motion that has randomness arising from their many collisions with each other and with the walls of the container.It will applicable only for gases
Question 7
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The number of degrees of freedom a monatomic molecule is

A
2

B
1

C
3.0

D
4

Solution

Explanation:Degrees of freedom of a system refers to the possible independent motions a system can have.Monoatomic gas molecule can have 3 independent motion and hence have 3 degrees of freedom (all are translational).
Question 8
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Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by 2.00 K.

A
85.0 J

B
95.0 J

C
65.0 J

D
75.0 J

Solution

Explanation:
Helium is a monoatomic gas.(C_V= 1.5R)
change in internal energy
ΔU=nCVΔT=3×1.5×8.31×2=75J
Question 9
1 / -0

One mole of an ideal monatomic gas is at an initial temperature of 300 K. The gas undergoes an isovolumetric process, acquiring 500 J of energy by heat. It then undergoes an isobaric process, losing this same amount of energy by heat. Determine the work done on the gas.

A
123 J

B
231 J

C
333 J

D
200 J

Solution

Explanation:
At const volume,
Q = 500 J
Q=nCPΔT
500=1×2.5×8.31ΔT
ΔT=24.06
W=nRΔT=1×8.31×24.06=200J
Question 10
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Kinetic theory relates measurable properties.

A
of liquids such as viscosity, conduction and diffusion with molecular parameters, yielding estimates of molecular sizes and masses

B
of super cooled liquids such as viscosity, creep and diffusion with molecular parameters, yielding estimates of molecular sizes and masses

C
of solids such as expansion, conduction and elongation with molecular parameters, yielding estimates of molecular sizes and masses

D
of gases such as viscosity, conduction and diffusion with molecular parameters, yielding estimates of molecular sizes and masses

Solution

Explanation:Kinetic theory explains the behaviour of gases based on the idea that the gas consists of rapidly moving atoms or molecules. It also relates measurable properties of gases such as viscosity, conduction and diffusion with molecular parameters, yielding estimates of molecular sizes and masses.
Question 11
1 / -0

Mean free path is the

A
maximum distance between collisions

B
minimum distance between collisions

C
average distance between collisions

D
(maximum distance + minimum distance )/ 2 between collisions

Solution

Explanation:the mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties.
Question 12
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According to Atomic Hypothesis:

A
All things are made of atoms - little particles that keep oscillating

B
All things are made of atoms - little particles that stay put at fixed points

C
All things are made of atoms - little particles that move around in perpetual motion

D
All things are made of atoms - little particles that move around in circles

Solution

Explanation:atomic hypothesis that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.
Question 13
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1 mole of a monoatomic gas is mixed with 3 moles of a diatomic gas. What is the molecular specific heat of the mixture at constant volume?

A
12.5 J / mol K

B
18.7 J / mol K

C
15.2 J / mol K

D
22.6 J / mol K

Solution

Explanation:
for monoatomic gas

from conservation of energy
Question 14
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According to Avogadro’s law:

A
Equal volumes of all gases at equal temperature and pressure have different number of molecules.

B
Equal volumes of all gases at equal temperature and pressure have the same number of molecules.

C
Equal volumes of all gases at equal temperature have the same number of molecules.

D
Equal volumes of all gases at equal pressure have the same number of molecules.

Solution

Explanation:Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules"For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.
Question 15
1 / -0

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
3.86 kJ

B
3.49 kJ

C
3.66 kJ

D
3.26 kJ

Solution

Explanation:
Hydrogen is a diatomic gas. (C_P= 3.5R)
energy transferred by heat to the gas
Q=nCPΔT=1×3.5×8.31×120=3490J=3.49KJ
Question 16
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In which case are the atoms relatively rigidly fixed?

A
gases

B
liquids and gases

C
solids

D
liquids

Solution

Explanation:
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.
Question 17
1 / -0

One mole of hydrogen gas is heated at constant pressure from 300 K to 420 K. Calculate the increase in its internal energy.

A
2.49 kJ

B
2.65 kJ

C
2.15 kJ

D
2.85 kJ

Solution

Explanation:
Hydrogen is a diatomic gas. (C_V= 2.5R)
Change in internal energy
ΔU = nCVΔT = 1 x 2.5 x 8.31 x 120 = 2493J = 2.49KJ
Question 18
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Two moles of an ideal gas (γ=1.4) expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. What is the final pressure of the gas?

A
1.59 atm

B
1.09 atm

C
1.19 atm

D
1.39 atm

Solution
Question 19
1 / -0

The average distance a molecule can travel without colliding is called the

A
mean free length

B
mean free path

C
mean free distance

D
mean free motion

Solution

Explanation:the mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties
Question 20
1 / -0

According to Atomic Hypothesis: little particles of atom

A
attract each other when they are at small distance apart, but repel upon being squeezed into one another

B
repel each other when they are at small distance apart, but attract upon being squeezed into one another

C
repel each other when they are at small distance apart, but repel upon being squeezed into one another

D
repel each other when they are at large distance apart, but attract upon being separated from one another

Solution

Explanation:At room temperature (=300K) the noble gases are all in the gas phase, they are banging around and colliding into one another like little pool balls. At this temperature, when the atoms collide they appear to elastically bounce off of one another, but this bounce is actually a result of atomic repulsion. The atoms are traveling so fast and they approach each other so quickly that their momentum 'squeezes' them together until the atomic repulsion pushes them back apart.
Question 21
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In dynamic equilibrium, molecules collide and change their speeds during the collision

A
but the average properties vary.

B
but the average properties are constant.

C
but the peak properties vary.

D
but the r.m.s properties vary.

Solution

Explanation:All collisions between molecules among themselves or between molecules and the walls are elastic. So that total kinetic energy and total momentum is conserved. Also the average properties of gas are remains constant.
Question 22
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One mole of hydrogen gas is heated at constant pressure from 300 K to 420 K. Calculate the work done by the gas.

A
0.98kJ

B
1.27 kJ

C
1.11 kJ

D
0.93 kJ

Solution

Explanation:
In isobaric process
W=nR(TF−TI)=1×8.31×(420−300)=0.98kJ
Question 23
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The average kinetic energy of a molecule

A
is proportional to the absolute temperature of the gas

B
is inversely proportional to the absolute temperature of the gas

C
is inversely proportional to the molecular mass of the gas

D
is not dependent on absolute temperature of the gas

Solution

Explanation:
Question 24
1 / -0

Figure shows plot of PV/T versus P for 1.00x10^-3 kg of oxygen gas at two different temperatures. What is the value of PV/T where the curves meet on the y-axis?

A
0.24 J K⁻¹

B
0.22 J K⁻¹

C
0.26 J K⁻¹

D
0.28 J K⁻¹

Solution

PV=nRT
Hence the value of PV/T where the curves meet on the y-axis is 0.26 jK^-1
Question 25
1 / -0

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. find the particles’ average speed.

A
16.7 m/s

B
10.7 m/s

C
12.7 m/s

D
8.7 m/s

Solution
Question 26
1 / -0

What is the root-mean-square speed of helium atoms in a balloon of diameter 30.0 cm at 20.0⁰C and 1.00 atm?

A
1.49 km/s

B
1.35 km/s

C
1.57 km/s

D
1.15 km/s

Solution

= 1351m/sec = 1.35 Km/sec
Question 27
1 / -0

For a rope of yield strength Sy loaded in tension with weight Mg the minimum area A of the rope should be

A
A ≥ Mg/2 Sy

B
A ≥ Mg Sy

C
A ≥ Mg/ Sy

D
A ≥ Mg/3 Sy

Solution

F = YA (∆l/l)
F = Mg, Y = Sy, A = A using this we get
So, Mg ≤ Sy x A => A ≥ Mg/Sy
Question 28
1 / -0

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapor and other constituents) in a room of capacity 25.0 m³ at a temperature of 27⁰C and 1 atm pressure.

A
6.50 x 10²⁶

B
6.60 x 10²⁶

C
6.10 x 10²⁶

D
6.30 x 10²⁶

Solution
Question 29
1 / -0

In a 30.0-s interval, 500 hailstones strike a glass window with an area of 0.600 m² at an angle of 45.0° to the window surface. Each hailstone has a mass of 5.00 g and a speed of 8.00 m/s. If the collisions are elastic, what is the pressure on the window?

A
1.97 Pa

B
1.57 Pa

C
1.13 Pa

D
1.32 Pa

Solution
Question 30
1 / -0

Four liters of a diatomic ideal gas ( λ =1.4) confined to a cylinder is subject to a closed cycle. Initially, the gas is at 1.00 atm and at 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. Find the temperature at the end of the cycle

A
276 K

B
285 K

C
300 K

D
332 K

Solution

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