Question 1

The rms speed of a certain sample of carbon dioxide molecules, with a molecular weight of 44 g/mole is 396 m/s. What is the rms speed of water molecules, with a molecular weight of 18 g/mol at the same temperature?
A) 253 m/s
B) 387 m/s
C) 421 m/s
D) 506 m/s
E) 619 m/s

Accepted Answer

The answer of The rms speed of a certain sample...

Question 2

A 1200-kg car is being raised with a constant acceleration of 2.53 m/s² by a crane, using a 20-m long steel cable, 1.5 cm in diameter. Young's modulus for steel is 20 × 10¹⁰ N/m². What is the change in length of the cable? A) 8.4 mm B) 8.4 cm C) 4.9 mm D) 4.9 cm E) 4.9 m

Accepted Answer

The change in length of the cable can be calculated using the formula for elongation: ΔL = (F * L) / (A * Y), where F is the force, L is the original length, A is the cross-sectional area, and Y is Young's modulus. The force F is the sum of gravitational force and the force due to acceleration: F = m(g + a). The cross-sectional area A = π(d/2)^2. Substituting the values, the change in length ΔL is approximately 8.4 mm.

Question 3

Opposing shearing forces of 3000 N are applied to the 4.00 cm × 5.00 cm faces of a 3.00 cm × 4.00 cm × 5.00 cm steel block. By what amount does the block become slanted? The shear modulus for steel is 8.10 × 10¹⁰ N/m². A) 1.54 × 10^-6 m B) 5.56 × 10^-7 m C) 9.88 × 10^-7 m D) 3.08 × 10^-6 m E) 6.98 × 10^-6 m

Accepted Answer

The answer of Opposing shearing forces of 3000 N are...

Question 4

At what temperature is the rms speed of hydrogen molecules, which have a molecular weight of 2.02 g/mole, equal to 2000 m/s?
A) 17.0°C
B) 34.0°C
C) 51.0°C
D) 68.0°C
E) 72.0°C

Accepted Answer

The answer of At what temperature is the rms speed...

Question 5

What is the internal energy in 2.7 moles of hydrogen at 300 K? As an approximation, treat the hydrogen gas as if it was monatomic.
A) 10 kJ
B) 12 kJ
C) 14 kJ
D) 16 kJ
E) 18 kJ

Accepted Answer

The internal energy of a monatomic ideal gas is given by:$$U = \frac{3}{2}nRT$$where:* $U$ is the internal energy in joules* $n$ is the number of moles of gas* $R$ is the ideal gas constant ($8.314 \ J/mol \ K$)* $T$ is the temperature in kelvinsPlugging in the given values, we get:$$U = \frac{3}{2}(2.7 \ mol)(8.314 \ J/mol \ K)(300 \ K) = 10.0 kJ$$Therefore, the internal energy in 2.7 moles of hydrogen at 300 K is 10 kJ.

Question 6

A 50-kg air conditioner is placed on top of a concrete pad with a cross-sectional area of 3.0 m² and 20 cm thick. What is the change in thickness of the pad? Young's modulus for concrete is 2.3 × 10¹⁰ N/m². A) 1.4 × 10^-9 m B) 2.8 × 10^-9 m C) 1.4 × 10^-8 m D) 1.4 × 10^-7 m E) 2.8 × 10^-8 m

Accepted Answer

The change in thickness (ΔL) can be calculated using the formula ΔL = (F * L) / (A * Y), where F is the force (weight of the air conditioner), L is the original thickness, A is the area, and Y is Young's modulus. Here, F = 50 kg * 9.8 m/s² = 490 N, L = 0.2 m, A = 3.0 m², and Y = 2.3 × 10¹⁰ N/m². Substituting these values gives ΔL = (490 * 0.2) / (3.0 * 2.3 × 10¹⁰) = 1.4 × 10⁻⁹ m.

Question 7

Opposing shearing forces of 3000 N are applied to the 3.00 cm × 4.00 cm faces of a 3.00 cm × 4.00 cm × 5.00 cm steel block. By what amount does the block become slanted? The shear modulus for steel is 8.0 × 10¹⁰ N/m². A) 1.54 × 10^-6 m B) 5.56 × 10^-7 m C) 9.88 × 10^-7 m D) 3.08 × 10^-6 m E) 6.98 × 10^-⁶ m

Accepted Answer

The shear strain is given by:$$\gamma = \frac{F}{A}\frac{1}{G}$$where:* F is the force applied* A is the area of the face* G is the shear modulusPlugging in the given values, we get:$$\gamma = \frac{3000 	ext{ N}}{(0.03 	ext{ m})(0.04 	ext{ m})}\frac{1}{8.0 	imes 10^{10} 	ext{ N/m}^2} = 1.54 	imes 10^{-6} 	ext{ m}$$The amount the block becomes slanted is given by:$$	heta = \gamma h$$where:* h is the height of the blockPlugging in the given values, we get:$$	heta = (1.54 	imes 10^{-6} 	ext{ m})(0.05 	ext{ m}) = 7.70 	imes 10^{-8} 	ext{ rad}$$

Question 8

What is the root mean square value of the following velocity components: 2.0 m/s, -3.0 m/s, and 4.0 m/s?
A) 5.4 m/s
B) 1.9 m/s
C) 3.1 m/s
D) 3.3 m/s
E) 1.0 m/s

Accepted Answer

The root-mean-square (rms) value of a set of values is calculated by taking the square root of the average of the squares of the values. For the velocity components 2.0 m/s, -3.0 m/s, and 4.0 m/s, the calculation is as follows: sqrt[(2.0^2 + (-3.0)^2 + 4.0^2) / 3] = sqrt[(4 + 9 + 16) / 3] = sqrt[29 / 3] ≈ 3.1 m/s.

Question 9

What is the average kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is 17°C? A) 6.01 × 10^-21 J B) 4.00 × 10^-21 J C) 5.00 × 10^-21 J D) 7.00 × 10^-21 J E) 9.00 × 10^-21 J

Accepted Answer

The average kinetic energy of a molecule is given by (3/2)kT, where k is the Boltzmann constant (1.38 × 10^-23 J/K) and T is the temperature in Kelvin. Converting 17°C to Kelvin gives 290 K. Plugging in the values, the average kinetic energy is approximately 6.01 × 10^-21 J.

Question 10

A 30-cm steel rod, 1.0 cm in diameter, supports a 300-kg mass. What is the change in length of the rod? Young's modulus for steel is 20 × 10¹⁰ N/m². A) 5.6 × 10^-5 m B) 6.5 × 10^-5 m C) 5.6 × 10^-6 m D) 6.5 × 10^-6 m E) 6.5 × 10^-4 m

Accepted Answer

The change in length is calculated using the formula ΔL = (F*L) / (A*Y), where F = mg = 300*9.8 N, L = 0.3 m, A = π*(0.005 m)^2, and Y = 20 × 10^10 N/m². This gives ΔL ≈ 5.6 × 10^-5 m.

Question 11

The molecular weight of carbon dioxide is 44.0 g/mol. What is the internal energy in 3.00 kg of carbon dioxide at 300 K? As an approximation, treat the carbon dioxide gas as if it was monatomic. A) 2.55 × 10⁵ J B) 1.70 × 10⁵ J C) 2.55 × 10⁴ J D) 1.70 × 10⁴ J E) 1.70 × 10⁶ J

Accepted Answer

The internal energy of a monatomic gas can be calculated using the formula:

U = (3/2)NkT

where
U = internal energy
N = number of particles (in this case, we can use Avogadro's number to convert from mass to number of particles)
k = Boltzmann's constant
T = temperature

First, we need to calculate the number of particles in 3.00 kg of carbon dioxide:

n = (3.00 kg) / (44.0 g/mol) * (1 mol / 6.022 * 10^23 particles) = 1.70 * 10^25 particles

Then, we can plug in the values into the formula:

U = (3/2) * (1.70 * 10^25) * (1.38 * 10^-23 J/K) * (300 K) = 2.55 * 10^14 J

Using scientific notation, the answer is 2.55 × 10^14 J, which corresponds to choice A.

Question 12

When a mixture of gases is placed in a container at a given temperature, the pressure in the container is equal to the sum of the pressures that the individual gases would exert if they separately occupied the entire container at the same temperature. Given that air is basically a mixture of nitrogen, with a molecular weight of 28 g/mol, and oxygen, with a molecular weight of 32 g/mol, what must be the ratio of the mass of oxygen to the mass of nitrogen in air for air to have an effective molecular weight of 29?
A) 8:21
B) 3:5
C) 5:7
D) 32:87
E) 3:7

Accepted Answer

To find the ratio of the mass of oxygen to nitrogen, use the formula for the effective molecular weight: $ M = xN_2 \cdot 28 + xO_2 \cdot 32 $, where $ xN_2 $ and $ xO_2 $ are the mole fractions. Solving for the given effective molecular weight of 29, the ratio of the mass of oxygen to nitrogen is 8:21.

Question 13

A quantity of an ideal gas is kept in a rigid container of constant volume. If the gas is originally at a temperature of 19°C, at what temperature will the pressure of the gas double from its base value?
A) 91°C
B) 38°C
C) 311°C
D) 273°C
E) 122°C

Accepted Answer

According to Gay-Lussac's law, for a gas at constant volume, the pressure is directly proportional to its temperature in Kelvin. If the pressure doubles, the temperature in Kelvin must also double. The initial temperature is 19°C, which is 292K. Doubling this gives 584K, which is 311°C.

Question 14

A 200-kg superhero, falling off a building manages to grab hold of the end of a 3.0 m-long flagpole, 5.0 cm in radius, which saves him from falling any further. After the oscillations have died down, the end of the flagpole is sagging 10 cm. What is the shear modulus of the pole? A) 7.5 × 10⁶ N/m² B) 2.4 × 10⁶ N/m² C) 7.5 × 10⁷ N/m² D) 2.4 × 10⁷ N/m² E) 2.4 × 10⁵ N/m²

Accepted Answer

The shear modulus is given by:$$S=\frac{3mgL}{4\pi r^3	heta}$$where:* S is the shear modulus* m is the mass of the superhero* g is the acceleration due to gravity* L is the length of the flagpole* r is the radius of the flagpole* θ is the angle of deflectionPlugging in the given values, we get:$$S=\frac{3(200	ext{ kg})(9.8	ext{ m/s}^2)(3.0	ext{ m})}{4\pi(0.05	ext{ m})^3(0.10	ext{ rad})}$$$$S=7.5	imes10^6	ext{ N/m}^2$$Therefore, the correct answer is A.

Question 15

A 25-kg television set rests on four rubber pads, each having a height of 1.0 cm and a radius of 0.60 cm. A horizontal force is applied to the television set. When the pads are at the point of sliding, how far has the television set moved sideways? The coefficient of friction between the rubber and the floor is 1.0 and the shear modulus of rubber is 2.6 × 10⁶ N/m². A) 16 mm B) 8.4 mm C) 4.2 mm D) 2.1 mm E) 1.1 mm

Accepted Answer

The answer of A 25-kg television set rests on four...

Question 16

What is the root mean square value of the following speeds: 2.0 m/s, 3.0 m/s, 4.0 m/s?
A) 1.0 m/s
B) 2.8 m/s
C) 2.9 m/s
D) 3.0 m/s
E) 3.1 m/s

Accepted Answer

The root mean square speed is calculated as the square root of the average of the squares of the speeds: sqrt((2^2 + 3^2 + 4^2)/3) = sqrt((4 + 9 + 16)/3) = sqrt(29/3) = sqrt(9.67) ≈ 3.1 m/s.

Question 17

A 1200-kg car is being raised at a constant speed by a crane, using a 20-m long steel cable, 1.50 cm in diameter. Young's modulus for steel is 20 × 10¹⁰ N/m². What is the change in length of the cable? A) 6.7 mm B) 6.7 cm C) 3.3 mm D) 3.3 cm E) 3.3 m

Accepted Answer

The change in length of the cable can be calculated using the formula for linear deformation: ΔL = (F * L) / (A * Y), where F is the force (weight of the car), L is the original length of the cable, A is the cross-sectional area, and Y is Young's modulus. The force is the weight of the car (1200 kg * 9.8 m/s²), the area is π*(0.015/2)² m², and Young's modulus is 20 × 10¹⁰ N/m². Solving gives approximately 6.7 mm.

Question 18

A 25-kg television set rests on four rubber pads, each having a height of 1.0 cm and a radius of 0.60 cm. A 200-N horizontal force is applied to the television set. How far does it move sideways? The shear modulus of rubber is 2.6 × 10⁶ N/m². A) 6.8 mm B) 3.4 mm C) 1.7 mm D) 1.5 mm E) 1.3 mm

Accepted Answer

The shear deformation can be calculated using the formula: deformation = (force * height) / (shear modulus * area). The area of one pad is π * (0.006 m)^2. The total area for four pads is 4 * π * (0.006 m)^2. Substituting the values, the deformation is approximately 1.7 mm.

Question 19

The molecular weight of nitrogen is 28 g/mol. What is the rms speed of nitrogen molecules at 8.0°C?
A) 450 m/s
B) 500 m/s
C) 550 m/s
D) 600 m/s
E) 650 m/s

Accepted Answer

The rms speed of a gas molecule is given by the formula: $ v_{rms} = \sqrt{\frac{3kT}{m}} $, where $ k $ is the Boltzmann constant, $ T $ is the temperature in Kelvin, and $ m $ is the mass of one molecule. Converting 8.0°C to Kelvin gives 281 K. Using the molecular weight of nitrogen (28 g/mol), the rms speed is approximately 500 m/s.

Question 20

A copper sphere, 10 cm in diameter, is subjected to a pressure of 1.0 × 10⁶ N/m². What is the change in the diameter of the sphere? The bulk modulus for copper is 1.4 × 10¹⁰ N/m². A) 2.2 × 10^-6 m B) 2.2 × 10^-7 m C) 7.1 × 10^-6 m D) 7.1 × 10^-7 m E) 7.1 × 10^-8 m

Accepted Answer

The answer of A copper sphere, 10 cm in diameter,...

Quiz 17: Phases and Phase Changes

The rms speed of a certain sample of carbon dioxide molecules, with a molecular weight of 44 g/mole is 396 m/s. What is the rms speed of water molecules, with a molecular weight of 18 g/mol at the same temperature?

A 1200-kg car is being raised with a constant acceleration of 2.53 m/s2 by a crane, using a 20-m long steel cable, 1.5 cm in diameter. Young's modulus for steel is 20 × 1010 N/m2. What is the change in length of the cable?

Opposing shearing forces of 3000 N are applied to the 4.00 cm × 5.00 cm faces of a 3.00 cm × 4.00 cm × 5.00 cm steel block. By what amount does the block become slanted? The shear modulus for steel is 8.10 × 1010 N/m2.

At what temperature is the rms speed of hydrogen molecules, which have a molecular weight of 2.02 g/mole, equal to 2000 m/s?

What is the internal energy in 2.7 moles of hydrogen at 300 K? As an approximation, treat the hydrogen gas as if it was monatomic.

A 50-kg air conditioner is placed on top of a concrete pad with a cross-sectional area of 3.0 m2 and 20 cm thick. What is the change in thickness of the pad? Young's modulus for concrete is 2.3 × 1010 N/m2.

Opposing shearing forces of 3000 N are applied to the 3.00 cm × 4.00 cm faces of a 3.00 cm × 4.00 cm × 5.00 cm steel block. By what amount does the block become slanted? The shear modulus for steel is 8.0 × 1010 N/m2.

What is the root mean square value of the following velocity components: 2.0 m/s, -3.0 m/s, and 4.0 m/s?

What is the average kinetic energy of a nitrogen molecule in the air in a room in which the air temperature is 17°C?

A 30-cm steel rod, 1.0 cm in diameter, supports a 300-kg mass. What is the change in length of the rod? Young's modulus for steel is 20 × 1010 N/m2.

The molecular weight of carbon dioxide is 44.0 g/mol. What is the internal energy in 3.00 kg of carbon dioxide at 300 K? As an approximation, treat the carbon dioxide gas as if it was monatomic.

A quantity of an ideal gas is kept in a rigid container of constant volume. If the gas is originally at a temperature of 19°C, at what temperature will the pressure of the gas double from its base value?

A 200-kg superhero, falling off a building manages to grab hold of the end of a 3.0 m-long flagpole, 5.0 cm in radius, which saves him from falling any further. After the oscillations have died down, the end of the flagpole is sagging 10 cm. What is the shear modulus of the pole?

What is the root mean square value of the following speeds: 2.0 m/s, 3.0 m/s, 4.0 m/s?

A 1200-kg car is being raised at a constant speed by a crane, using a 20-m long steel cable, 1.50 cm in diameter. Young's modulus for steel is 20 × 1010 N/m2. What is the change in length of the cable?

A 25-kg television set rests on four rubber pads, each having a height of 1.0 cm and a radius of 0.60 cm. A 200-N horizontal force is applied to the television set. How far does it move sideways? The shear modulus of rubber is 2.6 × 106 N/m2.

The molecular weight of nitrogen is 28 g/mol. What is the rms speed of nitrogen molecules at 8.0°C?

A copper sphere, 10 cm in diameter, is subjected to a pressure of 1.0 × 106 N/m2. What is the change in the diameter of the sphere? The bulk modulus for copper is 1.4 × 1010 N/m2.

A 1200-kg car is being raised with a constant acceleration of 2.53 m/s² by a crane, using a 20-m long steel cable, 1.5 cm in diameter. Young's modulus for steel is 20 × 10¹⁰ N/m². What is the change in length of the cable?

Opposing shearing forces of 3000 N are applied to the 4.00 cm × 5.00 cm faces of a 3.00 cm × 4.00 cm × 5.00 cm steel block. By what amount does the block become slanted? The shear modulus for steel is 8.10 × 10¹⁰ N/m².

A 50-kg air conditioner is placed on top of a concrete pad with a cross-sectional area of 3.0 m² and 20 cm thick. What is the change in thickness of the pad? Young's modulus for concrete is 2.3 × 10¹⁰ N/m².

Opposing shearing forces of 3000 N are applied to the 3.00 cm × 4.00 cm faces of a 3.00 cm × 4.00 cm × 5.00 cm steel block. By what amount does the block become slanted? The shear modulus for steel is 8.0 × 10¹⁰ N/m².

A 30-cm steel rod, 1.0 cm in diameter, supports a 300-kg mass. What is the change in length of the rod? Young's modulus for steel is 20 × 10¹⁰ N/m².

A 1200-kg car is being raised at a constant speed by a crane, using a 20-m long steel cable, 1.50 cm in diameter. Young's modulus for steel is 20 × 10¹⁰ N/m². What is the change in length of the cable?

A 25-kg television set rests on four rubber pads, each having a height of 1.0 cm and a radius of 0.60 cm. A 200-N horizontal force is applied to the television set. How far does it move sideways? The shear modulus of rubber is 2.6 × 10⁶ N/m².

A copper sphere, 10 cm in diameter, is subjected to a pressure of 1.0 × 10⁶ N/m². What is the change in the diameter of the sphere? The bulk modulus for copper is 1.4 × 10¹⁰ N/m².