Question 1

Suppose the interaction between two atoms has the effective potential energy curve shown below:
  
I have marked the vertical scale on this graph using an arbitrary energy unit we'll call bondits.
- Suppose we know that the system has 5 bondits of kinetic energy when its atoms are separated by $0.2 \mathrm{~nm}$. What minimum energy is required to break the bond?

Accepted Answer

(Since the system's potential energy is -15 bondits at a separation of 0.2 nm, the
system's total energy must be (5 - 15) bondits = -10 bondits. To break the bond, we must
increase the system's energy above the peak in the potential energy at r = 0.5 nm. Since this
peak has an energy of 5 bondits, we must increase the system's energy by 15 bondits.)

Question 2

Suppose the interaction between two atoms has the effective potential energy curve shown below:
  
I have marked the vertical scale on this graph using an arbitrary energy unit we'll call bondits.
-Suppose instead we know that at $t=0$ the atoms are at rest at a separation of $0.4 \mathrm{~nm}$. What minimum energy is required to break the bond in this case?

Accepted Answer

(If the system is at rest at r = 0.4 nm, then its total energy is zero. Increasing the
system's energy above the peak at r = 0.5 nm requires 5 bondits of energy.)

Question 3

Suppose the interaction between two atoms has the effective potential energy curve shown below:
  
I have marked the vertical scale on this graph using an arbitrary energy unit we'll call bondits.
-If the atoms have 10 bondits of kinetic energy at infinity, what energy must we remove to form a bond?

Accepted Answer

(If the system has 10 bondits of kinetic energy at infinity (where the potential energy is
zero), then its total energy must also be 10 bondits. To form the bond, we must reduce the
system's energy below the outer peak at r = 0.5 nm, that is, below 5 bondits. This will require
reducing the system's energy by at least 5 bondits.)

Question 4

Suppose we put a $0.3-\mathrm{kg}$ hunk of ice at $0^{\circ} \mathrm{C}$ into an insulating thermos bottle filled with $1000 \mathrm{~g}$ of water at $20^{\circ} \mathrm{C}$. What will be the system's final temperature?

Accepted Answer

The heat lost by the water will be equal to the heat gained by the ice. The heat lost by the water is:$$Q_w = m_w c_w (T_i - T_f)$$where $m_w$ is the mass of the water, $c_w$ is the specific heat of water, $T_i$ is the initial temperature of the water, and $T_f$ is the final temperature of the system.The heat gained by the ice is:$$Q_i = m_i L_f + m_i c_i (T_f - T_i)$$where $m_i$ is the mass of the ice, $L_f$ is the latent heat of fusion of ice, $c_i$ is the specific heat of ice, and $T_i$ is the initial temperature of the ice.Setting $Q_w = Q_i$, we get:$$m_w c_w (T_i - T_f) = m_i L_f + m_i c_i (T_f - T_i)$$Solving for $T_f$, we get:$$T_f = \frac{m_w c_w T_i + m_i L_f + m_i c_i T_i}{m_w c_w + m_i c_i}$$Plugging in the numbers, we get:$$T_f = \frac{(1000 \mathrm{~g})(4.187 \mathrm{~J/g \degree C})(20^{\circ} \mathrm{C}) + (300 \mathrm{~g})(334 \mathrm{~J/g}) + (300 \mathrm{~g})(2.09 \mathrm{~J/g \degree C})(0^{\circ} \mathrm{C})}{(1000 \mathrm{~g})(4.187 \mathrm{~J/g \degree C}) + (300 \mathrm{~g})(2.09 \mathrm{~J/g \degree C})}$$$$T_f = 0.1^{\circ} \mathrm{C}$$Therefore, the final temperature of the system will be almost exactly $0^{\circ} \mathrm{C}$.

Question 5

The thermal energy of a block of ice at $0^{\circ} \mathrm{C}$ melting to a puddle of water at $0^{\circ} \mathrm{C}$ in a cup at room temperature

Accepted Answer

The thermal energy of the ice and water is the same, since the temperature does not change.

Question 6

An egg will cook no more rapidly in furiously boiling water than in gently simmering water

Accepted Answer

Both furiously boiling water and gently simmering water are at the same temperature (100°C or 212°F at sea level), so the egg will cook at the same rate in either condition. The intensity of the boil does not increase the water's temperature due to water's boiling point limit at atmospheric pressure.

Question 7

A 100-g sample of a certain substance undergoes a transformation of some kind that releases 20,000 $\mathrm{J}$ of energy. What kind of transformation is this likely to be?

Accepted Answer

The answer of A 100-g sample of a certain substance...

Question 8

Suppose you climb about 10 stories worth of stairs. Roughly what is the minimum number of food calories you have burned? (Select the closest.)

Accepted Answer

The answer of Suppose you climb about 10 stories worth...

Question 9

If the sound level increases by 20 decibels, by about how much has the intensity of sound (in $\mathrm{W} / \mathrm{m}^{2}$ ) increased?

Accepted Answer

The intensity of sound increases by a factor of 10 for every 10 decibels increase, so a 20 decibels increase means the intensity increases by a factor of 10^2 = 100 times.

Question 10

Suppose sand is leaking from an unpowered but moving railroad car. Since the sand is moving forward along with the car as it leaks out, it carries kinetic energy out of the car. This mass transfer will

Accepted Answer

The car's speed remains unchanged because the sand's forward momentum is transferred to the ground, not affecting the car's velocity.

Question 11

Suppose an unpowered but moving railroad car receives some coal (basically at rest) from a stationary conveyor belt. This coal therefore only carries chemical energy into the car. This mass transfer will

Accepted Answer

When coal is transferred to the moving railroad car, the total mass of the car increases. According to the principle of conservation of momentum, if no external force acts on the system, the total momentum of the system (car plus coal) before and after the coal transfer remains constant. Since momentum is the product of mass and velocity, an increase in the mass (due to the addition of coal) without an increase in the system's total momentum means the velocity (speed) of the car must decrease.

Question 12

According to the Stefan-Boltzmann law, an object at room temperature that is sitting in a room (also at room temperature) must emit electromagnetic radiation. Since it is losing energy by emitting this radiation, why does its temperature remain constant?

Accepted Answer

The answer of According to the Stefan-Boltzmann law, an object...

Question 13

The emergency blankets in some first-aid kits consist of very thin Mylar that has been coated with aluminum to make it shiny. How can such thin plastic be a blanket?
- Which mechanism of a person's heat loss is most effectively suppressed by the blanket?

Accepted Answer

Emergency blankets, also known as space blankets, are effective in reducing heat loss primarily through radiation. The shiny aluminum coating reflects the body's heat back towards the person, rather than allowing it to radiate away into the environment. This reflective property makes them particularly useful in preventing hypothermia by conserving the body's radiant heat.

Question 14

The emergency blankets in some first-aid kits consist of very thin Mylar that has been coated with aluminum to make it shiny. How can such thin plastic be a blanket?
-Which mechanism does it least effectively suppress?

Accepted Answer

The thin Mylar emergency blankets are designed to reflect body heat back to the user, effectively suppressing heat loss through radiation. However, they are less effective at suppressing heat loss through conduction, as they are very thin and do not provide much insulation against direct contact with cold surfaces.

Question 15

Suppose a star has twice the surface temperature of the sun and also twice the radius. How many times larger is the rate at which this star emits energy compared to the rate at which the sun emits energy?

Accepted Answer

The rate at which a star emits energy is given by the Stefan-Boltzmann Law: $ L = 4\pi R^2 \sigma T^4 $. If the star has twice the surface temperature (T) and twice the radius (R) of the sun, the luminosity becomes $ L = 4\pi (2R)^2 \sigma (2T)^4 = 16 \times 4\pi R^2 \sigma T^4 = 64 \times L_{\text{sun}} $. Thus, the star emits energy 64 times more than the sun.

Question 16

A small person with a surface area of about $1.0 \mathrm{~m}^{2}$ must (by the Stefan-Boltzmann law) radiate energy at a rate that would require eating 11,000 food calories a day if they are naked in a vacuum in deep space. Which do you think is the most important reason that someone sitting in a normal room requires less than 2000 calories a day?

Accepted Answer

The most important reason someone in a normal room requires less than 2000 calories a day, compared to the scenario of being naked in a vacuum, is that the person absorbs radiation from the room. This significantly reduces the net loss of energy through radiation, as the Stefan-Boltzmann law considers both emission and absorption. In a normal room, the walls, objects, and air are at a similar temperature to the human body, leading to a balance between the energy radiated by the body and the energy absorbed from the surroundings.

Question 17

A dark object sitting in sunlight gets warm. The sun radiates light because it is very hot, much hotter than the object. So should we categorize the radiation that the object receives from the sun as being heat $Q$ or energy transferred by electromagnetic radiation $\left[E_{\mathrm{ER}}\right]$ ? Be prepared to justify your answer with an argument (multiple reasonable arguments are possible).

Accepted Answer

The answer of A dark object sitting in sunlight gets...

Question 18

Kepler's 3rd law applies to hyperbolic orbits.

Accepted Answer

Kepler's 3rd law specifically applies to elliptical orbits, not hyperbolic orbits. Hyperbolic orbits do not exhibit the periodic behavior that Kepler's laws describe for elliptical orbits around a focal point.

Question 19

Water slowly evaporates from your skin.

Accepted Answer

The answer of Water slowly evaporates from your skin.
...

Question 20

You can be certain that a collision between two objects is elastic if

Accepted Answer

In an elastic collision, not only is the total momentum of the system conserved, but the total kinetic energy of the system is also conserved. Choices A and B are necessary conditions for any type of collision (elastic or inelastic), but not sufficient to ensure the collision is elastic. Choice D is misleading because the physical property of being "bouncy or springy" does not guarantee the conservation of kinetic energy. Choice E describes a perfectly inelastic collision, the opposite of an elastic collision.

Quiz 1: Conservation Laws Constrain Interactions

Suppose the interaction between two atoms has the effective potential energy curve shown below: I have marked the vertical scale on this graph using an arbitrary energy unit we'll call bondits. -If the atoms have 10 bondits of kinetic energy at infinity, what energy must we remove to form a bond?

Suppose we put a $0.3-\mathrm{kg}$ hunk of ice at $0^{\circ} \mathrm{C}$ into an insulating thermos bottle filled with $1000 \mathrm{~g}$ of water at $20^{\circ} \mathrm{C}$ . What will be the system's final temperature?

The thermal energy of a block of ice at $0^{\circ} \mathrm{C}$ melting to a puddle of water at $0^{\circ} \mathrm{C}$ in a cup at room temperature

An egg will cook no more rapidly in furiously boiling water than in gently simmering water

A 100-g sample of a certain substance undergoes a transformation of some kind that releases 20,000 $\mathrm{J}$ of energy. What kind of transformation is this likely to be?

Suppose you climb about 10 stories worth of stairs. Roughly what is the minimum number of food calories you have burned? (Select the closest.)

If the sound level increases by 20 decibels, by about how much has the intensity of sound (in $\mathrm{W} / \mathrm{m}^{2}$ ) increased?

Suppose sand is leaking from an unpowered but moving railroad car. Since the sand is moving forward along with the car as it leaks out, it carries kinetic energy out of the car. This mass transfer will

Suppose an unpowered but moving railroad car receives some coal (basically at rest) from a stationary conveyor belt. This coal therefore only carries chemical energy into the car. This mass transfer will

According to the Stefan-Boltzmann law, an object at room temperature that is sitting in a room (also at room temperature) must emit electromagnetic radiation. Since it is losing energy by emitting this radiation, why does its temperature remain constant?

The emergency blankets in some first-aid kits consist of very thin Mylar that has been coated with aluminum to make it shiny. How can such thin plastic be a blanket? - Which mechanism of a person's heat loss is most effectively suppressed by the blanket?

The emergency blankets in some first-aid kits consist of very thin Mylar that has been coated with aluminum to make it shiny. How can such thin plastic be a blanket? -Which mechanism does it least effectively suppress?

Suppose a star has twice the surface temperature of the sun and also twice the radius. How many times larger is the rate at which this star emits energy compared to the rate at which the sun emits energy?

Kepler's 3rd law applies to hyperbolic orbits.

Water slowly evaporates from your skin.

You can be certain that a collision between two objects is elastic if

Quiz 1: Conservation Laws Constrain Interactions

Suppose the interaction between two atoms has the effective potential energy curve shown below: I have marked the vertical scale on this graph using an arbitrary energy unit we'll call bondits. -If the atoms have 10 bondits of kinetic energy at infinity, what energy must we remove to form a bond?

Suppose we put a 0.3−kg0.3-\mathrm{kg}0.3−kg hunk of ice at 0∘C0^{\circ} \mathrm{C}0∘C into an insulating thermos bottle filled with 1000 g1000 \mathrm{~g}1000 g of water at 20∘C20^{\circ} \mathrm{C}20∘C . What will be the system's final temperature?

The thermal energy of a block of ice at 0∘C0^{\circ} \mathrm{C}0∘C melting to a puddle of water at 0∘C0^{\circ} \mathrm{C}0∘C in a cup at room temperature

An egg will cook no more rapidly in furiously boiling water than in gently simmering water

A 100-g sample of a certain substance undergoes a transformation of some kind that releases 20,000 J\mathrm{J}J of energy. What kind of transformation is this likely to be?

Suppose you climb about 10 stories worth of stairs. Roughly what is the minimum number of food calories you have burned? (Select the closest.)

If the sound level increases by 20 decibels, by about how much has the intensity of sound (in W/m2\mathrm{W} / \mathrm{m}^{2}W/m2 ) increased?

Suppose sand is leaking from an unpowered but moving railroad car. Since the sand is moving forward along with the car as it leaks out, it carries kinetic energy out of the car. This mass transfer will

Suppose an unpowered but moving railroad car receives some coal (basically at rest) from a stationary conveyor belt. This coal therefore only carries chemical energy into the car. This mass transfer will

According to the Stefan-Boltzmann law, an object at room temperature that is sitting in a room (also at room temperature) must emit electromagnetic radiation. Since it is losing energy by emitting this radiation, why does its temperature remain constant?

The emergency blankets in some first-aid kits consist of very thin Mylar that has been coated with aluminum to make it shiny. How can such thin plastic be a blanket? - Which mechanism of a person's heat loss is most effectively suppressed by the blanket?

The emergency blankets in some first-aid kits consist of very thin Mylar that has been coated with aluminum to make it shiny. How can such thin plastic be a blanket? -Which mechanism does it least effectively suppress?

Suppose a star has twice the surface temperature of the sun and also twice the radius. How many times larger is the rate at which this star emits energy compared to the rate at which the sun emits energy?

Kepler's 3rd law applies to hyperbolic orbits.

Water slowly evaporates from your skin.

You can be certain that a collision between two objects is elastic if

Suppose we put a $0.3-\mathrm{kg}$ hunk of ice at $0^{\circ} \mathrm{C}$ into an insulating thermos bottle filled with $1000 \mathrm{~g}$ of water at $20^{\circ} \mathrm{C}$ . What will be the system's final temperature?

The thermal energy of a block of ice at $0^{\circ} \mathrm{C}$ melting to a puddle of water at $0^{\circ} \mathrm{C}$ in a cup at room temperature

A 100-g sample of a certain substance undergoes a transformation of some kind that releases 20,000 $\mathrm{J}$ of energy. What kind of transformation is this likely to be?

If the sound level increases by 20 decibels, by about how much has the intensity of sound (in $\mathrm{W} / \mathrm{m}^{2}$ ) increased?