Ultimate Astronomy

Question 1

A filament's initial temperature is 4000K. The filament temperature is then adjusted to 5000K by turning a knob. There is more red light emanating from the filament.

Accepted Answer

Finally, when it is at 5000K

Answer

The question states that the filament temperature is adjusted to 5000K, and *then* there is more red light emanating. This directly links the observation of increased red light to the final temperature of 5000K. While hotter objects shift their peak emission to bluer wavelengths (Wien's Law), they also emit more radiation at *all* wavelengths, including red, compared to when they were cooler (Stefan-Boltzmann Law).

Question 2

Imagine a star with the same temperature on its surface but twice the sun's surface area. What is the energy flux at that star's surface if the energy flux at the sun's surface is Fsun?

Accepted Answer

Fsun

Answer

Energy flux is defined as the amount of energy emitted per unit surface area. According to the Stefan-Boltzmann Law, this flux depends solely on the surface temperature of the object (F = σT^4). Since the star has the same surface temperature as the Sun, its energy flux at the surface will be identical to the Sun's, regardless of its total surface area.

Question 3

Imagine a star that is twice as big as the sun and has the same surface temperature. What is the total energy emitted by a star per second if the sun emits P watts of energy every second?

Accepted Answer

2 P Watts

Answer

The total energy emitted by a star per second (luminosity) is the energy flux multiplied by its total surface area. If the star has the same surface temperature as the Sun, its energy flux (energy per square meter) is the same. The term 'twice as big' in this context refers to having twice the surface area. Therefore, if the star has twice the surface area, it will emit twice the total energy (2 * P Watts).

Question 4

How much more total radiated power per square meter (energy Flux) would we receive on Earth if the sun's temperature doubled?

Accepted Answer

Sixteen times (2^4)

Answer

According to the Stefan-Boltzmann Law, the total radiated power per square meter (energy flux, F) is directly proportional to the fourth power of the object's absolute temperature (F = σT^4). If the Sun's temperature (T) were to double (2T), the new flux would be σ(2T)^4 = σ * 16 * T^4. This means the energy flux would increase by a factor of sixteen (2^4).

Question 5

The surface of the sun is a good representation of a black body. Let's say the temperature of the sun doubled overnight. In that case, which of the following claims would be accurate?

Accepted Answer

The sun would look bluer and radiate more power

Answer

If the Sun's temperature doubled, two key physical laws apply. Wien's Displacement Law states that the peak wavelength of emitted radiation shifts to shorter (bluer) wavelengths as temperature increases, so the Sun would look bluer. Simultaneously, the Stefan-Boltzmann Law dictates that the total power radiated per unit area is proportional to the fourth power of the temperature, meaning a doubled temperature would result in significantly more power radiated (16 times more).

Astronomy Practice Test

Astronomy Practice Test

Ultimate Astronomy