   Chapter 19, Problem 42E

Chapter
Section
Textbook Problem

# The earth receives 1.8 × 1014 kJ/s of solar energy. What mass of solar material is converted to energy over a 24-h period to provide the daily amount of solar energy to the earth? What mass of coal would have to be burned to provide the same amount of energy? (Coal releases 32 kJ of energy per gram when burned.)

Interpretation Introduction

Interpretation: The amount of solar energy received by earth is given. Mass of solar energy converted to energy over a 24 -hour period to provide the daily amount of solar energy to the earth is to be calculated. Mass of coal required to be burned to provide the same amount of energy is to be stated.

Concept introduction: Energy change of a system can be calculated by Einstein’s theory of relativity. When a system loses or gains energy, it also gains or loses a quantity of mass given by E/c2 .

To determine: Mass of solar energy converted to energy over a 24 -hour period to provide the daily amount of solar energy to the earth and the mass of coal required to be burned to provide the same amount of energy.

Explanation

Explanation

Mass lost is calculated by the Einstein mass energy equation, that is,

ΔE=ΔmC2

Where,

• ΔE is the change in energy.
• Δm is the change in mass.
• C is the velocity of light.

Substitute the values of ΔE and C in the equation.

ΔE=ΔmC2Δm=ΔEC2Δm=1.8×10179×1016=2kg

The mass lost in 24 hours is calculated by the formula,

24×3600×2=172800Kg_

Explanation

Given

The solar energy received by the Earth is 1.8×1014kJ/s .

The conversion of seconds into hours is,

1s=13600h

Therefore, the conversion of 1.8×1014kJ/s into kJ/h is,

1.8×1014kJ/s=(1.8×1014×3600)kJ/h

The conversion of hours into days is,

1day=24h

Therefore, the conversion of (1

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