Question 1

Two identical solid spheres have the same temperature. One of the spheres is cut into two identical pieces. These two hemispheres are then separated. The intact sphere radiates an energy Q during a given time interval. During the same interval, the two hemispheres radiate a total energy Q'. What is the ratio Q'/Q?

Accepted Answer

The radiation energy is proportional to the surface area. The intact sphere has a surface area of 4πr². When cut into two hemispheres, the total surface area becomes 2(2πr²) = 4πr² (curved surfaces) + 2(πr²) (flat surfaces) = 6πr². Thus, the ratio of the radiated energy is 6πr²/4πr² = 1.5.

Question 2

If a beaker of water is placed under a broiler so that the heating coil is above the beaker. It is observed that only the surface layer boils. The water at the bottom of the beaker remains close to the initial temperature of the water. Which of the following statements is the most reasonable conclusion to be drawn from these observations?

Accepted Answer

The observation that only the surface layer boils while the water at the bottom remains close to its initial temperature suggests that heat is not being conducted well throughout the water. This is consistent with the fact that water is a poor conductor of heat, as heat is primarily transferred through convection in water.

Question 3

Object A has an emissivity of 0.95; and its temperature is 25 °C. At what temperature (in degrees Celsius) does object B, whose emissivity is 0.50, emit radiation at the same rate as object A if both objects have the same surface area?

Accepted Answer

The answer of Object A has an emissivity of 0.95;...

Question 4

The power radiated by a distant star is 6.2 × 10²⁷ W. The radius of the star, which may be considered a perfect radiator, is 1.06 × 10¹⁰ m. Determine the surface temperature of the star.

Accepted Answer

The answer of The power radiated by a distant star...

Question 5

Complete the following statement: The interior of a thermos bottle is silvered to minimize heat transfer due to

Accepted Answer

The interior of a thermos bottle is silvered to minimize heat transfer due to radiation. The silver coating reflects back the heat radiation, reducing the amount of heat transferred through radiation.

Question 6

Complete the following statement: Most of the heat that is lost to space from the earth occurs by

Accepted Answer

Heat is lost from the Earth through radiation as it emits longwave radiation, or infrared radiation, out to space. This is why the Earth's surface cools at night, as it radiates its heat away into space. The other options, conduction and convection, involve the transfer of heat through direct contact or movement of matter, and are not as significant in heat loss to space.

Question 7

A blue supergiant star has a radius of 7.4 × 10¹⁰ m. The spherical surface behaves as a blackbody radiator. If the surface temperature is 2.4 × 10⁴ K, what is the rate at which energy is radiated from the star?

Accepted Answer

The rate of energy radiated by a blackbody is given by the Stefan-Boltzmann law: P = σA(T^4), where σ is the Stefan-Boltzmann constant (5.67 × 10^-8 W/m²K⁴), A is the surface area (4πr²), and T is the temperature. Calculating with the given values results in approximately 1.3 × 10^33 J/s.

Question 8

A hot metal ball is hung in an oven that is maintained at 700 K; and it cools. When the temperature of the ball is 950 K, it is losing heat at a rate of 0.15 J/min. At what rate will the ball lose heat when the ball reaches 820 K? Assume that the emissivity of the ball and its surface area do not change appreciably with temperature.

Accepted Answer

The rate of heat loss for an object can be described by the Stefan-Boltzmann law, which states that the power radiated (or the rate of heat loss) is proportional to the fourth power of the absolute temperature of the object. Given that the rate of heat loss at 950 K is 0.15 J/min, we can use the ratio of the fourth powers of the temperatures to find the rate at 820 K: (820/950)^4 * 0.15 J/min = 0.08 J/min.

Question 9

Which one of the following statements concerning the Stefan-Boltzmann equation is true?

Accepted Answer

The Stefan-Boltzmann equation can be used to calculate the power emitted by any surface, regardless of whether it is a perfect radiator or absorber. It describes the relationship between the temperature of an object and the amount of thermal radiation it emits. It is valid with any temperature units, as long as they are consistent. The equation does not describe the transport of thermal energy by conduction, which is described by Fourier's law.

Question 10

Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 mS1U1P12S1S1P0, are placed end to end as shown in the figure.  The thermal conductivities of the bars are
kS1U1B1AS1U1B0 = 439 J/(s . m . K) and kS1U1B1BS1U1B0 = 887 J/(s . m . K), respectively. The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K.
-How much heat passes the interface between A and B in 6.0 s?

Accepted Answer

We can use Fourier's law of heat conduction:

Q = -kA(dT/dx)t

where Q is the heat transfer rate, k is the thermal conductivity, A is the cross-sectional area, (dT/dx)t is the temperature gradient at the interface between the bars, and the negative sign indicates that heat flows from the hot end to the cold end.

We can assume that the temperature gradient is constant along the length of each bar, so (dT/dx)t is simply the temperature difference divided by the length of each bar. Thus:

Q = -kA[(373-273)/2.0 + (273-373)/2.0]/0.06 = -439*1.0*(100.0/2.0 + 100.0/2.0)/0.06 -887*1.0*(100.0/2.0 + 100.0/2.0)/0.06 = 8.8×10^14 J

The negative sign means that heat flows from A to B, so the heat transferred across the interface is:

|Q| = 8.8×10^14 J

Therefore, the answer is (D).

Question 11

Which one of the following objects, all initially at the same temperature, will be most efficient in losing heat?

Accepted Answer

A dull black box in air will be most efficient in losing heat because dull black surfaces are good emitters of radiation, and the presence of air allows for additional heat loss through convection, making it more efficient in losing heat compared to the other options.

Question 12

Two bars, A and B, each of length 2.0 m and cross sectional area 1.0 mS1U1P12S1S1P0, are placed end to end as shown in the figure.  The thermal conductivities of the bars are
kS1U1B1AS1U1B0 = 439 J/(s . m . K) and kS1U1B1BS1U1B0 = 887 J/(s . m . K), respectively. The left end of bar A is maintained at 373 K while the right end of B is maintained at 273 K.
-What is the rate of heat transfer through this combination?

Accepted Answer

The answer of Two bars, A and B, each of...

Question 13

A beaker of water is placed on a Bunsen burner. As the lower layers of water are heated, they become less dense and rise. This permits cooler layers to move downward and be heated. Eventually, the water boils. Which method(s) of heat transfer is (are) primarily responsible for boiling the sample?

Accepted Answer

The primary methods of heat transfer responsible for boiling the water are conduction and convection. Conduction occurs as heat is transferred from the Bunsen burner to the beaker and then to the water at the bottom. Convection currents are created as the heated water rises and cooler water moves down to be heated, circulating heat throughout the beaker.

Question 14

Which one of the following statements concerning emissivity is false?

Accepted Answer

Emissivity does not depend on the surface area of the object, but rather on the material and condition of the surface.

Question 15

Assume that the sun is a sphere of radius 6.96 × 10⁸m and that its surface temperature is 5.8 × 10³ K. If the sun radiates at a rate of 3.90 × 10²⁶ W and is a perfect emitter, at what rate is energy emitted per square meter at the sun's surface?

Accepted Answer

The rate at which energy is emitted per square meter at the sun's surface can be calculated using the Stefan-Boltzmann law:

E = σT^4

where E is the energy emitted per square meter per second, σ is the Stefan-Boltzmann constant (5.67 × 10^-8 W/m^2K^4), and T is the temperature in Kelvin.

Plugging in the given values, we get:

E = (5.67 × 10^-8 W/m^2K^4)(5.8 × 10^6 K)^4
  = 6.4 × 10^7 W/m^2

Therefore, the answer is (B) 6.4 × 10^17 W/m^2.

Question 16

Which one of the following graphs shows the rate at which heat is emitted from a hot body as a function of its Kelvin temperature T?

Accepted Answer

The answer of Which one of the following graphs shows...

Question 17

Which object will emit more electromagnetic radiation than it absorbs from its surroundings?

Accepted Answer

The answer of Which object will emit more electromagnetic radiation...

Question 18

A person steps out of the shower and dries off. The person's skin with an emissivity of 0.70 has a total area of 1.2 m² and a temperature of 33 °C. What is the net rate at which energy is lost to the room through radiation by the naked person if the room temperature is 24 °C?

Accepted Answer

The answer of A person steps out of the shower...

Question 19

The sun continuously radiates energy into space in all directions. Some of the sun's energy is intercepted by the earth. The average temperature of the surface of the earth remains a little above 300 K. Why doesn't the earth's temperature rise as it intercepts the sun's energy?

Accepted Answer

The earth radiates an amount of energy into space equal to the amount it receives. This is known as the energy balance of the earth. The energy from the sun is absorbed by the earth's surface and then radiated back into space in the form of infrared radiation. This radiation keeps the earth's temperature stable, as the amount of energy absorbed by the earth is equal to the amount of energy radiated back into space. If the earth were to absorb more energy than it radiates, its temperature would rise.

Question 20

Assuming a filament in a 100 W light bulb acts like a perfect blackbody, what is the temperature of the hottest portion of the filament if it has a surface area of 6.3 × 10^-⁵ m²? The Stefan-Boltzmann constant is 5.67 × 10^-⁸ W/(m² · K²).

Accepted Answer

Using the Stefan-Boltzmann law, P = σAeT^4, where P is power, σ is the Stefan-Boltzmann constant, A is area, and T is temperature. Solving for T gives approximately 2300 K.

Quiz 13: The Transfer of Heat

Object A has an emissivity of 0.95; and its temperature is 25 °C. At what temperature (in degrees Celsius) does object B, whose emissivity is 0.50, emit radiation at the same rate as object A if both objects have the same surface area?

The power radiated by a distant star is 6.2 × 10²⁷ W. The radius of the star, which may be considered a perfect radiator, is 1.06 × 10¹⁰ m. Determine the surface temperature of the star.

Complete the following statement: The interior of a thermos bottle is silvered to minimize heat transfer due to

Complete the following statement: Most of the heat that is lost to space from the earth occurs by

A blue supergiant star has a radius of 7.4 × 10¹⁰ m. The spherical surface behaves as a blackbody radiator. If the surface temperature is 2.4 × 10⁴ K, what is the rate at which energy is radiated from the star?

Which one of the following statements concerning the Stefan-Boltzmann equation is true?

Which one of the following objects, all initially at the same temperature, will be most efficient in losing heat?

A beaker of water is placed on a Bunsen burner. As the lower layers of water are heated, they become less dense and rise. This permits cooler layers to move downward and be heated. Eventually, the water boils. Which method(s) of heat transfer is (are) primarily responsible for boiling the sample?

Which one of the following statements concerning emissivity is false?

Assume that the sun is a sphere of radius 6.96 × 10⁸m and that its surface temperature is 5.8 × 10³ K. If the sun radiates at a rate of 3.90 × 10²⁶ W and is a perfect emitter, at what rate is energy emitted per square meter at the sun's surface?

Which one of the following graphs shows the rate at which heat is emitted from a hot body as a function of its Kelvin temperature T?

Which object will emit more electromagnetic radiation than it absorbs from its surroundings?

A person steps out of the shower and dries off. The person's skin with an emissivity of 0.70 has a total area of 1.2 m² and a temperature of 33 °C. What is the net rate at which energy is lost to the room through radiation by the naked person if the room temperature is 24 °C?

The sun continuously radiates energy into space in all directions. Some of the sun's energy is intercepted by the earth. The average temperature of the surface of the earth remains a little above 300 K. Why doesn't the earth's temperature rise as it intercepts the sun's energy?

Assuming a filament in a 100 W light bulb acts like a perfect blackbody, what is the temperature of the hottest portion of the filament if it has a surface area of 6.3 × 10^-⁵ m²? The Stefan-Boltzmann constant is 5.67 × 10^-⁸ W/(m² · K²) .

Quiz 13: The Transfer of Heat

Object A has an emissivity of 0.95; and its temperature is 25 °C. At what temperature (in degrees Celsius) does object B, whose emissivity is 0.50, emit radiation at the same rate as object A if both objects have the same surface area?

The power radiated by a distant star is 6.2 × 1027 W. The radius of the star, which may be considered a perfect radiator, is 1.06 × 1010 m. Determine the surface temperature of the star.

Complete the following statement: The interior of a thermos bottle is silvered to minimize heat transfer due to

Complete the following statement: Most of the heat that is lost to space from the earth occurs by

A blue supergiant star has a radius of 7.4 × 1010 m. The spherical surface behaves as a blackbody radiator. If the surface temperature is 2.4 × 104 K, what is the rate at which energy is radiated from the star?

Which one of the following statements concerning the Stefan-Boltzmann equation is true?

Which one of the following objects, all initially at the same temperature, will be most efficient in losing heat?

A beaker of water is placed on a Bunsen burner. As the lower layers of water are heated, they become less dense and rise. This permits cooler layers to move downward and be heated. Eventually, the water boils. Which method(s) of heat transfer is (are) primarily responsible for boiling the sample?

Which one of the following statements concerning emissivity is false?

Assume that the sun is a sphere of radius 6.96 × 108 m and that its surface temperature is 5.8 × 103 K. If the sun radiates at a rate of 3.90 × 1026 W and is a perfect emitter, at what rate is energy emitted per square meter at the sun's surface?

Which one of the following graphs shows the rate at which heat is emitted from a hot body as a function of its Kelvin temperature T?

Which object will emit more electromagnetic radiation than it absorbs from its surroundings?

A person steps out of the shower and dries off. The person's skin with an emissivity of 0.70 has a total area of 1.2 m2 and a temperature of 33 °C. What is the net rate at which energy is lost to the room through radiation by the naked person if the room temperature is 24 °C?

The sun continuously radiates energy into space in all directions. Some of the sun's energy is intercepted by the earth. The average temperature of the surface of the earth remains a little above 300 K. Why doesn't the earth's temperature rise as it intercepts the sun's energy?

Assuming a filament in a 100 W light bulb acts like a perfect blackbody, what is the temperature of the hottest portion of the filament if it has a surface area of 6.3 × 10-5 m2? The Stefan-Boltzmann constant is 5.67 × 10-8 W/(m2 · K2) .

The power radiated by a distant star is 6.2 × 10²⁷ W. The radius of the star, which may be considered a perfect radiator, is 1.06 × 10¹⁰ m. Determine the surface temperature of the star.

A blue supergiant star has a radius of 7.4 × 10¹⁰ m. The spherical surface behaves as a blackbody radiator. If the surface temperature is 2.4 × 10⁴ K, what is the rate at which energy is radiated from the star?

Assume that the sun is a sphere of radius 6.96 × 10⁸m and that its surface temperature is 5.8 × 10³ K. If the sun radiates at a rate of 3.90 × 10²⁶ W and is a perfect emitter, at what rate is energy emitted per square meter at the sun's surface?

A person steps out of the shower and dries off. The person's skin with an emissivity of 0.70 has a total area of 1.2 m² and a temperature of 33 °C. What is the net rate at which energy is lost to the room through radiation by the naked person if the room temperature is 24 °C?

Assuming a filament in a 100 W light bulb acts like a perfect blackbody, what is the temperature of the hottest portion of the filament if it has a surface area of 6.3 × 10^-⁵ m²? The Stefan-Boltzmann constant is 5.67 × 10^-⁸ W/(m² · K²) .