Using solar constant s = 20 kilo cal / mm - m´ and joule ' s constant ...
To find the pressure exerted by sunlight, we need to use the following formula:
The force exerted by sunlight is the power of sunlight (in joules/second) divided by the speed of light (in meters/second). The power of sunlight is equal to the solar constant (in calories/second/square meter) multiplied by the joule's constant (in joules/calorie).
So the force exerted by sunlight is:
Force = (Solar constant * Joule's constant)/(Speed of light)
= (20 * 4.2 * 1000)/(2.998 * 10^8)
= 0.0084 N/m^2
The area over which this force is applied is the surface area of the Earth. The surface area of the Earth is about 5.1 * 10^14 square meters.
So the pressure exerted by sunlight is:
= 0.0084/5.1 * 10^14
= 1.64 * 10^-11 N/m^2
The nearest integer to this value in 10^-6 N/m^2 is 16, so the answer is 16 * 10^-6 N/m^2.
This question is part of UPSC exam. View all JEE courses
Using solar constant s = 20 kilo cal / mm - m´ and joule ' s constant ...
Calculation of the pressure exerted by sunlight:
Solar constant:
The solar constant, denoted by 'S', is defined as the amount of solar radiation received per unit area per unit time at the outer atmosphere of the Earth. It represents the average amount of solar energy received on a unit area perpendicular to the Sun's rays at a mean distance from the Sun. The solar constant is given by the equation:
S = 20 kilo cal / mm² - m´
This means that for every square millimeter perpendicular to the Sun's rays, 20 kilocalories of solar energy is received per minute.
Joule's constant:
Joule's constant, denoted by 'J', is a conversion factor used to convert energy units. It is defined as the number of joules in one calorie. The value of Joule's constant is:
J = 4.2 J / cal
This means that 4.2 joules is equal to 1 calorie.
Conversion of solar constant to joules:
To find the pressure exerted by sunlight, we need to convert the solar constant from kilocalories to joules. We can use Joule's constant to do this conversion.
1 kilocalorie = 1000 calories
1 calorie = 4.2 joules
Therefore, 1 kilocalorie = 1000 * 4.2 joules = 4200 joules
Given that the solar constant is 20 kilocalories per mm² - m´, we can convert it to joules as follows:
20 kilocalories = 20 * 4200 joules = 84000 joules
Calculation of pressure:
Pressure is defined as force per unit area. In this case, the force is the solar radiation exerted by sunlight and the area is the surface perpendicular to the Sun's rays.
The pressure exerted by sunlight can be calculated using the formula:
Pressure = Force / Area
The force exerted by sunlight is the energy received per unit time, which is given by the solar constant. The area is the unit area perpendicular to the Sun's rays.
Given that the solar constant is 84000 joules and the area is 1 mm² - m´, we can calculate the pressure as follows:
Pressure = 84000 joules / (1 mm² - m´) = 84000 * 10^6 N / m² (since 1 mm = 10^-3 m)
Therefore, the pressure exerted by sunlight is approximately 84000 * 10^6 N / m², which is the nearest integer in 10^-6 N / m².
Summary:
- The solar constant represents the amount of solar energy received per unit area per unit time at the outer atmosphere of the Earth.
- Joule's constant is used to convert energy units.
- The solar constant is converted from kilocalories to joules using Joule's constant.
- The pressure exerted by sunlight is calculated by dividing the force (solar constant) by the area (unit area perpendicular to the Sun's rays).
- The pressure exerted by sunlight is approximately 84000 * 10^6 N / m², which is the nearest integer in 10^-6 N / m².
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.