Chapter 50, The Sun's Source of Power Video Solutions, Pathways to Astronomy

Problem 1

In chemical reactions, when energy is released, mass is lost according to Einstein's formula just as it is for nuclear energy (though the amounts lost are so small that for centuries scientists thought that mass was conserved). When a kilogram of coal is burned, it releases about 40 million joules of energy.
a. What amount of mass is lost?
b. How many carbon atoms (mass $=2.0 \times 10^{-26} \mathrm{kg}$ ) would it take to match the amount of mass that is lost?

Narayan Hari

Numerade Educator

02:21

Problem 2

Worldwide, humans use about $4 \times 10^{20}$ joules of energy each year. A typical power station generates about $10^{9}$ watts of power, while the Sun's luminosity is about $4 \times 10^{26}$ watts. (Recall that 1 watt $=1$ J/sec.)
a. How many power stations would be needed to produce power equivalent to the Sun's?
b. How many typical power stations are needed to supply current human energy usage?
c. If we could store all of the energy that the Sun produces in 1 second, how long would it last humans at current energy use rates?

Surjit Tewari

Numerade Educator

01:30

Problem 3

Using $E=m \times c^{2},$ calculate how much mass is turned into energy during a year by a typical power station. How much mass is turned into energy each year by worldwide energy usage? (Use the data given in problem 2.)

Suzanne W.

Numerade Educator

04:48

Problem 4

Assume that the Sun generates $4 \times 10^{26}$ watts throughout its lifetime. (Recall that $1 \mathrm{W}=1 \mathrm{J} / \mathrm{sec}$.)
a. How much mass will our Sun convert to energy over its entire main-sequence lifetime (10 $^{10}$ years)?
b. What fraction is this of the mass of the Sun?
c. How does this compare to the mass of the Earth?

Guilherme Barros

Numerade Educator

01:33

Problem 5

One "kiloton" of explosive energy is $4.2 \times 10^{12}$ joules. Using Einstein's formula, calculate the mass that is converted into energy in a 1 -megaton H-bomb explosion.

Narayan Hari

Numerade Educator

01:05

Problem 6

How long does it take a neutrino produced in the center of the Sun to reach the Sun's surface?

Mayukh Banik

Numerade Educator