Download Assignment #7

Assignment #7
Due November 8, 2000
Reading – very important!
1. Section 8-3 and 12-2
Understand figure 12-10
Window on Science 12-1
Critical Inquiry, p 168 and 233
2. Section 12-3: Stellar Structure – all of it.
Critical Inquiry, p 236
3. Section 13-1, 13-2 and 13-3 in detail!
Critical Inquiry, p 257, 262
Handouts!
Problems to hand in
1) Draw the HRD together with the evolutionary track of a solar mass star. Explain what
happens at every stage, and why this is so. (Comment on the energy source, and the fashion
in which energy gets transported to the surface. Also comment on the evolution of the core
of the star. Explain how the radius, luminosity and temperature change; ands also explain
why radius, luminosity and temperature change in that particular fashion.)
2) Look at figure 13-6 in your book. Comment on the evolutionary states of Betelgeuse, Rigel,
the Sun and Capella. Draw the same drawing, and then insert the evolutionary track of the
Sun.
Optional Problem
3) What is the energy source of the sun? The Sun’s mass, radius and luminosity are: R¤= 7
× 108 m, M¤= 2 × 1030 kg, L¤= 4 × 1026 W. (Hints: next page…)
a) Chemical Burning: The energy given off in coal burning, a typical chemical reaction, is
about 5 × 106 J/kg (that is 5 × 106 Joules per 1 kg of coal). If chemical burning were
the energy source in the Sun, calculate how much energy would be available. Then
calculate how long (in years) the sun would shine at its present luminosity? (Recall the
luminosity is defined as the energy emitted PER SECOND and is measured in Watts or
in Joules per second.)
b) The sun will burn roughly 10% of its entire hydrogen to helium. During this process
0.7% of that mass will get transformed into energy. If the solar energy is supplied via
nuclear burning, calculate how long (in years) the sun would shine at its present
luminosity.
Optional Essay
4. How do we know how stars evolve?
Hints to solving Problem 3a:
The energy given off in coal burning, a typical chemical reaction, is about 5 × 106 J/kg (that is 5
× 106 Joules per 1 kg of coal). If chemical burning were the energy source in the Sun, calculate
how much energy would be available.
•
This means that burning one kilo gram of coal gives off 5 × 106 Joules of Energy.
•
Look up the total mass of the Sun (in kilo grams) – given to be: M¤= 2 × 1030 kg
•
Figure out how much energy is released when burning 2 × 1030 kg of coal.
Then calculate how long (in years) the sun would shine at its present luminosity?
•
The Sun’s Luminosity is 4 × 1026 W. This means that the sun shines energy at a rate of 4
× 1026 Joules per second. You just calculated how much energy is produced when
burning coal – if this energy is released at a rate of 4 × 1026 Joules per second,
calculate how many seconds it would take for all that energy to be used up.
•
Then convert the number of seconds to years – this gives you the total lifetime of the
sun, if it was burning coal.
Hints to Solving Problem 3b:
The sun will burn roughly 10% of its entire hydrogen to helium. During this process 0.7% of that
mass will get transformed into energy. If the solar energy is supplied via nuclear burning,
calculate how long (in years) the sun would shine at its present luminosity.
•
Calculate mass to be concerted to energy:
Total mass of sun to be converted to Helium: 10%
Mass being lost that is transformed into energy: 0.7%
Calculate total mass that is transformed, i.e. is multiply the solar mass by 0.7% and then
by 10%.
•
Calculate to how much energy (in Joules) this corresponds
Mass converted to energy via: E=mc2
•
How long does the sun shine?
Answer like in part (a): The Sun’s Luminosity is 4 × 1026 Watts. This means that the
sun shines energy at a rate of 4 × 1026 Joules per second. You just calculated how
much energy is produced – if this energy is released at a rate of 4 × 1026 Joules per
second, calculate how many seconds it would take for all that energy to be used up.
Then convert the number of seconds to years – this gives you the total lifetime of the
sun.