Radiant Energy Formula

Have you at any point thought about how soil helps in promoting the growth of plants? Soil assimilates energy and the light and heat absorption warms seeds and roots in the soil to promote growth also plants can saddle and use light energy in a process called photosynthesis. They assimilate the energy from daylight into useful chemical energy contained in molecules within their cells. Creatures can get a portion of this substance energy as food by eating plants, or by eating creatures that eat different creatures or plants, and this energy from the sun is called Radiant energy.

What is Radiant Energy?

Radiant energy is the energy that travels by waves or particles, especially electromagnetic radiation such as gamma rays, x-rays, radio frequencies, microwaves, light, and heat which might be portrayed with regards to either discrete packets of energy, called photons, or consistent electromagnetic waves. Radiant energy is also known as electromagnetic radiation (EMR).

Not all radiant energy is apparent. Only photons inside a tiny scope of energies should be visible to individuals, normally known as visible light. Photons with lower energies are found in microwaves, radio waves, and infrared radiation. Photons with higher energies are found in bright beams, x-beams, and gamma beams.Radiant energy is one of the forms whose particles can move within a vacuum quite efficiently.

Basically whatever has a temperature emits radiant energy. A few instances of radiant energy include:

• The hotness is transmitted from an open-air fire.
• A surface warmed by the sun changes over the energy of the light into infrared energy which is a type of radiant energy.
• Sound transmissions that come to home or vehicles through radio waves.
• The heat is generated by a light bulb.
• The heat is emitted from a bunsen burner, computer, and washing machine.
• Heat is created from a stove or oven.
• Heat is generated through the reflection of visible light.
• Naturally occurring radiant energy includes Gamma rays, Radio waves, Heat caused by friction, and Ultraviolet light.
• Thermal energy stations use radiation to bubble water driving steam turbines.
• Sun-based power(solar power) harvests radiant energy conveyed by the light from our sun by changing it over it into electricity.
• Radioisotope thermal generators utilize radiant energy from a radioactive source to gather heat or even make power.
• Radiant energy and its ways of behaving have been bridled in numerous creations from the light bulb to the huge hadron collider.

Formula for Radiant Energy 

The Radiant heat energy is a thought which is fairly more well-made sense of by Stefan’s Boltzmann law. This regulation clarifies how the heat is transmitted!

It states that the amount of heat that is radiated (E) by a flawless black body for a second in a provided unit area is directly related to the fourth power of its absolute temperature (T).

The Radiant heat energy formula is,

E α T⁴

or 

E = σ T⁴

where 

• σ is Stefan’s constant (5.67 × 10 W/m²/K⁴),
• E is the Radiant energy.
• T is the Absolute temperature.

The SI unit of radiant energy is Joule (J).

Sample Questions 

Question 1: Assuming the temperature of the Sun was to increment from T to 3T, then the proportion of the radiant energy got on Earth to what it recently was?

Answer: 

Given that, 

Temperature is equal to 3T.

Here we have to find the Proportion of radiant energy.

The formula for Radiant energy is 

E = σ T⁴

E₂ = σ(3T)⁴

E/E₂ = σ T⁴/σ81T⁴

E/E₂ = 1/81

Hence, the proportion of the radiant energy got on Earth to what it recently is 1:81.

Question 2: The temperature of the fire in a heater is 2300 K, find the total radiant energy transmitted/m².

Answer:

Given that, 

The temperature is equal to 2300K.

Here we have to find the Radiant energy.

The formula for Radiant energy is 

E = σ T⁴

Since, σ = 5.67 × 10⁻⁸.

E = 5.67 × 10⁻⁸ × (2300)⁴

= 5.67 × (2300/100)⁴  

= 0.16 × 10⁷ 

Thus, the radiant energy is 0.16 × 10⁷ W/m².

Question 3: The surface temperature of the mars in the wintertime is 70 F. Figure the radiant energy for the 1 m² region.

Answer: 

Given that, 

The temperature is equal to 70°F.

The formula for Radiant energy is,

E = σ T⁴

Fahrenheit to kelvin formula is, 

(T)K = 5/9 [(T)F + 459.67]

(T)F = 70 F

(T)K = 5/9 [70 + 459.67] = 294.261 K

E = σ T⁴

Since, σ = 5.67 × 10⁻⁸

E = (5.67 × 10⁻⁸ ) × (294.26)⁴ 

= 425.11

Thus, the radiant energy is 425.11 W/m².

Question 4: The amount of power radiated by one square meter of the earth’s surface in 2021 is 319.58 W/m². Compute the temperature on earth’s surface temperature in Celsius.

Answer:

Given that, the Power radiated by one square meter (E) is 319.58 W/m².

Here we have to find the Temperature in Celsius.

The formula for the Radiant energy is,  

E = σ T⁴

Since, E = 319.58 W/m² and σ = 5.67 × 10⁻⁸ 

Therefore, 

T⁴ =  E/σ

319.58/5.67 × 10⁻⁸ = 5.636 × 10⁹

T(K) =  274 K

Celsius to kelvin : C = K – 273.15

C = 274 – 273.15 = 0.85

Thus the temperature is 0.85°C.

Question 5: The radiant energy from the sun, episode regularly at the outer layer of the earth, is 35 kcal/m² min. What might have been the radiant energy episode regularly on the earth, assuming the sun had a temperature one-half of the present one?

Answer:

Given that, the Radiant energy (E) is 35 kcal/m² min.

To find the sun’s temperature is one-half of the present one.

The formula for the Radiant energy is,

E = σ T⁴

As the temperature is one-half of the present one.

E₂ = σ(0.5T)⁴

Radiation falling on the earth will be relative to radiation being transmitted.

E/E₂  = σ T⁴/σ(0.5T)⁴

35/E₂ = 1/0.0625

E₂ = 35 × 0.0625 = 2.1875

Thus, the radiant energy is 2.1875 kcal/m² min.