Chapter 2: Q79E (page 67)

At Earth's location, the intensity of sunlight is 1.5 kW / $m^{2}$ . If no energy escaped Earth, by how much would Earth's mass increase in 1 day?

Short Answer

Expert verified

The increase in Earth’s mass for no escape of Sun’s energy from Earth is $7.34 \times 10^{5} kg$ .

Step by step solution

Identification of given data

The intensity of sunlight on Earth is $I = 1.5 kW / m^{2}$ .

The number of seconds in a day on Earth is $t = 1 day = 86400 s$ .

The energy received by Earth per unit surface area from the sun is called the solar constant.

Determination of energy received by Earth in one day

The energy received by Earth in time t is given as:

$E = I . A . t$

Here, A is the surface area of Earth and its value is $5.10 \times 10^{14} m^{2}$ .

For the given values, equation becomes-

$E = (1.5 kW / m^{2}) (\frac{10^{3} J / s}{1 kW}) (5.10 \times 10^{14}) (86400 s) E = 6.61 \times 10^{22} J$

Determination of increase in Earth’s mass

The increase in Earth’s mass is given as:

$E = m c^{2}$

Here, c is the speed of light in vacuum and its value is $3 \times 10^{8} m / s$

$6.61 \times 10^{22} J = m {(3 \times 10^{8} m / s)}^{2} m = 7.34 \times 10^{5} kg$

Therefore, the increase in Earth’s mass for no escape of energy from Earth is $7.34 \times 10^{5} kg$ .

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At Earth's location, the intensity of sunlight is 1.5 kW / $m^{2}$ . If no energy escaped Earth, by how much would Earth's mass increase in 1 day?

Short Answer

Step by step solution

Identification of given data

Determination of energy received by Earth in one day

Determination of increase in Earth’s mass

One App. One Place for Learning.

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At Earth's location, the intensity of sunlight is 1.5 kW / m2. If no energy escaped Earth, by how much would Earth's mass increase in 1 day?

Short Answer

Step by step solution

Identification of given data

Determination of energy received by Earth in one day

Determination of increase in Earth’s mass

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Famous Physicists

Fluids

Mechanics and Materials

Geometrical and Physical Optics

Work Energy and Power

Study anywhere. Anytime. Across all devices.

At Earth's location, the intensity of sunlight is 1.5 kW / $m^{2}$ . If no energy escaped Earth, by how much would Earth's mass increase in 1 day?