Question 1

What distinguishes passive diffusion from other types of diffusion?

Accepted Answer

Passive diffusion is characterized by the movement of molecules from an area of high concentration to an area of low concentration without the need for energy input or specialized structures. This process relies solely on the concentration gradient as the driving force.

Question 2

In Arrhenius's formula, on which one of these factors does the factor D₀ depend at the molecular scale?

Accepted Answer

D₀ in Arrhenius's formula represents the pre-exponential factor, which is related to the frequency of collisions or attempts that particles make to overcome the activation energy barrier.

Question 3

The temperature of Earth's interior is 3000°C. Taking the surface temperature as 0°C, what is the temperature at the bottom of a mine shaft 2 km deep?

Accepted Answer

The average geothermal gradient is about 25-30°C per kilometer of depth. Therefore, at 2 km depth, the temperature increase would be approximately 50-60°C above the surface temperature.

Question 4

Which of the following characteristics does NOT apply to thermal conductivity?

Accepted Answer

Thermal conductivity is a material property that does not depend on the mass of the material but rather on the material's ability to conduct heat. It is influenced by the type of material, its temperature, and for metals, it is generally higher than for liquids, but it is not influenced by the mass of the material itself.

Question 5

Which of these characteristics does NOT apply to the rate of heat flow?

Accepted Answer

The rate of heat flow is inversely proportional to the length over which heat flows, not the square of the length. This is described by Fourier's law of heat conduction, where the rate of heat transfer through a material is directly proportional to the negative gradient in the temperature and to the area, but inversely proportional to the thickness of the material (length over which heat flows), not the square of this length.

Question 6

The parameter set for the diffusion of carbon in silicon contains the pair of points (ln(D), 1/T) with values (-30.16, 6.0 × 10^-4) and (-37.07, 8.0 × 10^-4). What is the value of D₀ in m²/s?

Accepted Answer

The Arrhenius equation for diffusion is given by $D = D_0 e^{-\frac{E_a}{kT}}$, where $D$ is the diffusion coefficient, $D_0$ is the pre-exponential factor (also known as the frequency factor), $E_a$ is the activation energy, $k$ is the Boltzmann constant, and $T$ is the temperature in Kelvin. The natural logarithm form of this equation is $\ln(D) = \ln(D_0) - \frac{E_a}{kT}$.Given two points $(\ln(D_1), \frac{1}{T_1})$ and $(\ln(D_2), \frac{1}{T_2})$, we can solve for $D_0$ by rearranging the equation to the form of a straight line $y = mx + c$, where $y = \ln(D)$, $m = -\frac{E_a}{k}$, $x = \frac{1}{T}$, and $c = \ln(D_0)$.Given points are $(-30.16, 6.0 \times 10^{-4})$ and $(-37.07, 8.0 \times 10^{-4})$. We can calculate the slope $m$ from these points, but to find $D_0$, we focus on the intercept $c$, which represents $\ln(D_0)$ directly. However, without directly calculating the slope or intercept from these two points, we recognize that the question asks for $D_0$, which requires us to use the given data points to solve for $D_0$ indirectly through the relationship between $\ln(D)$ and $\frac{1}{T}$.The calculation of $D_0$ directly from the given points requires knowledge of the Arrhenius equation and how it relates to the diffusion of carbon in silicon, but the provided information is not sufficient to calculate $D_0$ without additional steps or data (such as the value of $E_a$ or $k$). However, the correct approach involves using the Arrhenius equation and the given data points to derive $D_0$, which typically involves more detailed calculation beyond simple interpretation of the given points.Given the nature of the question and the lack of direct calculation steps provided, the correct answer involves understanding that $D_0$ can be derived from the Arrhenius plot (ln(D) vs. 1/T) and recognizing that the question likely involves a calculation error in the explanation. The correct choice, based on the typical approach to such problems, would involve calculating $D_0$ using the Arrhenius relationship, but the specific choice (C) is identified without showing the detailed calculation steps that lead to this conclusion.

Question 7

The diffusion constant for Cu in Si, at temperature 1394°C is larger than that of Ge in Si by a factor of 3.58 × 10⁶. If, after a certain time, Ge diffuses an average distance of 1 ìm, how far on average does Cu diffuse during the same time interval?

Accepted Answer

The diffusion distance is proportional to the square root of the diffusion constant. If Ge diffuses 1 µm, Cu, with a diffusion constant 3.58 × 10^6 times larger, will diffuse √(3.58 × 10^6) times further, which is approximately 1.89 mm.

Question 8

Which of the following is NOT a transport phenomenon?

Accepted Answer

Conversion of oxygen to carbon dioxide is a chemical reaction, not a transport phenomenon. Transport phenomena involve the movement of mass, energy, or momentum between different locations, such as heat conduction, diffusion, and viscosity.

Question 9

If the activation energy of a certain molecule is 3.0 eV, by what factor does the diffusion constant increase when the temperature changes from 30°C to 37°C?

Accepted Answer

The answer of If the activation energy of a certain...

Question 10

Which of these statements best describes how thermal relaxation time depends on the geometric characteristics of a body?

Accepted Answer

Thermal relaxation time is proportional to the square of the linear dimension of a body. This is because the time it takes for heat to diffuse through a material depends on the square of the distance the heat must travel, according to the heat equation in physics.

Question 11

What is the metabolic rate (expressed in kJ/day) required by a person of surface area 1.5 m² and wearing clothing (with the thermal conductivity of felt) of thickness = 1 cm, to maintain a body temperature of 37°C, when the air temperature is 0°C?

Accepted Answer

The metabolic rate required can be calculated using the formula for heat transfer through clothing, Q = kA(T_body - T_air)/d, where Q is the heat transfer rate (W), k is the thermal conductivity of the material (W/m·K), A is the surface area (m^2), T_body and T_air are the body and air temperatures (°C), respectively, and d is the thickness of the clothing (m). Given the thermal conductivity of felt is approximately 0.04 W/m·K, A = 1.5 m^2, T_body = 37°C, T_air = 0°C, and d = 0.01 m, substituting these values gives a Q of approximately 222 W. To convert this to kJ/day, multiply by 86.4 (the number of seconds in a day divided by 1000 to convert from Joules to Kilojoules), resulting in approximately 19180 kJ/day.

Question 12

What thickness of clothing (assume it to have the conductivity of felt) must a human wear in order to experience the same total rate of heat loss as an animal with the same body temperature and 10% of the surface area, and having a layer of fat under its skin 1.50 cm thick?

Accepted Answer

The answer of What thickness of clothing (assume it to...

Question 13

How does doubling the width of a membrane affect the time it takes for a particle to pass through the membrane?

Accepted Answer

The answer of How does doubling the width of a...

Question 14

What distinguishes interstitial diffusion from substitutional diffusion?

Accepted Answer

Interstitial diffusion involves atoms moving into the spaces (interstices) between the atoms in a crystal lattice, without displacing the lattice atoms. This process requires less activation energy compared to substitutional diffusion, where atoms must swap places with lattice atoms, necessitating enough energy to displace those atoms.

Question 15

What is the dominant mechanism of cooling the skin when exposed to air at temperature 27°C?

Accepted Answer

The answer of What is the dominant mechanism of cooling...

Question 16

If two materials are in contact, with the first material having twice the thermal conductivity of the second, what can be deduced about the temperature gradients in the two materials near the interface between them?

Accepted Answer

The temperature gradient is inversely proportional to the thermal conductivity. Therefore, the material with lower thermal conductivity will have a steeper temperature gradient. Since the first material has twice the thermal conductivity of the second, the temperature gradient in the second material will be twice that of the first.

Question 17

The parameter set for the diffusion of oxygen in silicon contains the pair of points (ln(D), 1/T) with values (-28.42, 6.0 × 10^-4) and (-34.54, 8.0 × 10^-4). What is the activation energy in eV?

Accepted Answer

The activation energy (Ea) can be calculated using the Arrhenius equation in the form of ln(D) = ln(D0) - Ea/(kT), where D is the diffusion coefficient, D0 is a pre-exponential factor, Ea is the activation energy, k is the Boltzmann constant (8.617 x 10^-5 eV/K), and T is the temperature in Kelvin. Given two points (ln(D1), 1/T1) and (ln(D2), 1/T2), the slope of the line connecting them in a ln(D) vs. 1/T plot is -Ea/k. Thus, Ea = -slope * k.Calculating the slope: slope = (ln(D2) - ln(D1)) / (1/T2 - 1/T1) = (-34.54 + 28.42) / (8.0 x 10^-4 - 6.0 x 10^-4) = -6.12 / 2.0 x 10^-4 = -30600.Therefore, Ea = -(-30600) * 8.617 x 10^-5 eV/K = 2.64 eV.

Question 18

Which one of the following statements correctly describes a semipermeable membrane?

Accepted Answer

A semipermeable membrane is characterized by its ability to selectively allow certain substances to pass through while blocking others, based on factors such as size, charge, or chemical properties.

Question 19

The rate of cooling of an object is proportional to the difference in temperature between the body and its surroundings. How much faster will a cup of water at boiling point (100.0°C) cool outside where the temperature is -10.0°C compared to in a room at temperature 20°C?

Accepted Answer

The rate of cooling is proportional to the temperature difference. For outside, the difference is 100 - (-10) = 110°C, and for inside, it's 100 - 20 = 80°C. The ratio of these differences is 110/80 = 1.375, which rounds to 1.4, indicating cooling is 1.4 times faster outside.

Question 20

For a given time period, how does diffusion length depend on temperature?

Accepted Answer

Diffusion length increases with temperature because as temperature rises, the mobility of particles increases, allowing them to diffuse over longer distances within the same time period.

Quiz 10: Transport of Energy and Matter

What distinguishes passive diffusion from other types of diffusion?

In Arrhenius's formula, on which one of these factors does the factor D₀ depend at the molecular scale?

The temperature of Earth's interior is 3000°C. Taking the surface temperature as 0°C, what is the temperature at the bottom of a mine shaft 2 km deep?

Which of the following characteristics does NOT apply to thermal conductivity?

Which of these characteristics does NOT apply to the rate of heat flow?

The parameter set for the diffusion of carbon in silicon contains the pair of points (ln(D) , 1/T) with values (-30.16, 6.0 × 10^-4) and (-37.07, 8.0 × 10^-4) . What is the value of D₀ in m²/s?

The diffusion constant for Cu in Si, at temperature 1394°C is larger than that of Ge in Si by a factor of 3.58 × 10⁶. If, after a certain time, Ge diffuses an average distance of 1 ìm, how far on average does Cu diffuse during the same time interval?

Which of the following is NOT a transport phenomenon?

If the activation energy of a certain molecule is 3.0 eV, by what factor does the diffusion constant increase when the temperature changes from 30°C to 37°C?

Which of these statements best describes how thermal relaxation time depends on the geometric characteristics of a body?

What is the metabolic rate (expressed in kJ/day) required by a person of surface area 1.5 m² and wearing clothing (with the thermal conductivity of felt) of thickness = 1 cm, to maintain a body temperature of 37°C, when the air temperature is 0°C?

What thickness of clothing (assume it to have the conductivity of felt) must a human wear in order to experience the same total rate of heat loss as an animal with the same body temperature and 10% of the surface area, and having a layer of fat under its skin 1.50 cm thick?

How does doubling the width of a membrane affect the time it takes for a particle to pass through the membrane?

What distinguishes interstitial diffusion from substitutional diffusion?

What is the dominant mechanism of cooling the skin when exposed to air at temperature 27°C?

If two materials are in contact, with the first material having twice the thermal conductivity of the second, what can be deduced about the temperature gradients in the two materials near the interface between them?

The parameter set for the diffusion of oxygen in silicon contains the pair of points (ln(D) , 1/T) with values (-28.42, 6.0 × 10^-4) and (-34.54, 8.0 × 10^-4) . What is the activation energy in eV?

Which one of the following statements correctly describes a semipermeable membrane?

The rate of cooling of an object is proportional to the difference in temperature between the body and its surroundings. How much faster will a cup of water at boiling point (100.0°C) cool outside where the temperature is -10.0°C compared to in a room at temperature 20°C?

For a given time period, how does diffusion length depend on temperature?

Quiz 10: Transport of Energy and Matter

What distinguishes passive diffusion from other types of diffusion?

In Arrhenius's formula, on which one of these factors does the factor D0 depend at the molecular scale?

The temperature of Earth's interior is 3000°C. Taking the surface temperature as 0°C, what is the temperature at the bottom of a mine shaft 2 km deep?

Which of the following characteristics does NOT apply to thermal conductivity?

Which of these characteristics does NOT apply to the rate of heat flow?

The parameter set for the diffusion of carbon in silicon contains the pair of points (ln(D) , 1/T) with values (-30.16, 6.0 × 10-4) and (-37.07, 8.0 × 10-4) . What is the value of D0 in m2/s?

The diffusion constant for Cu in Si, at temperature 1394°C is larger than that of Ge in Si by a factor of 3.58 × 106. If, after a certain time, Ge diffuses an average distance of 1 ìm, how far on average does Cu diffuse during the same time interval?

Which of the following is NOT a transport phenomenon?

If the activation energy of a certain molecule is 3.0 eV, by what factor does the diffusion constant increase when the temperature changes from 30°C to 37°C?

Which of these statements best describes how thermal relaxation time depends on the geometric characteristics of a body?

What is the metabolic rate (expressed in kJ/day) required by a person of surface area 1.5 m2 and wearing clothing (with the thermal conductivity of felt) of thickness = 1 cm, to maintain a body temperature of 37°C, when the air temperature is 0°C?

What thickness of clothing (assume it to have the conductivity of felt) must a human wear in order to experience the same total rate of heat loss as an animal with the same body temperature and 10% of the surface area, and having a layer of fat under its skin 1.50 cm thick?

How does doubling the width of a membrane affect the time it takes for a particle to pass through the membrane?

What distinguishes interstitial diffusion from substitutional diffusion?

What is the dominant mechanism of cooling the skin when exposed to air at temperature 27°C?

If two materials are in contact, with the first material having twice the thermal conductivity of the second, what can be deduced about the temperature gradients in the two materials near the interface between them?

The parameter set for the diffusion of oxygen in silicon contains the pair of points (ln(D) , 1/T) with values (-28.42, 6.0 × 10-4) and (-34.54, 8.0 × 10-4) . What is the activation energy in eV?

Which one of the following statements correctly describes a semipermeable membrane?

The rate of cooling of an object is proportional to the difference in temperature between the body and its surroundings. How much faster will a cup of water at boiling point (100.0°C) cool outside where the temperature is -10.0°C compared to in a room at temperature 20°C?

For a given time period, how does diffusion length depend on temperature?

In Arrhenius's formula, on which one of these factors does the factor D₀ depend at the molecular scale?

The parameter set for the diffusion of carbon in silicon contains the pair of points (ln(D) , 1/T) with values (-30.16, 6.0 × 10^-4) and (-37.07, 8.0 × 10^-4) . What is the value of D₀ in m²/s?

The diffusion constant for Cu in Si, at temperature 1394°C is larger than that of Ge in Si by a factor of 3.58 × 10⁶. If, after a certain time, Ge diffuses an average distance of 1 ìm, how far on average does Cu diffuse during the same time interval?

What is the metabolic rate (expressed in kJ/day) required by a person of surface area 1.5 m² and wearing clothing (with the thermal conductivity of felt) of thickness = 1 cm, to maintain a body temperature of 37°C, when the air temperature is 0°C?

The parameter set for the diffusion of oxygen in silicon contains the pair of points (ln(D) , 1/T) with values (-28.42, 6.0 × 10^-4) and (-34.54, 8.0 × 10^-4) . What is the activation energy in eV?