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20191122

Astronomy midterm question: comparing sizes, temperatures of same-luminosity stars

Astronomy 210 Midterm 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

The following claim was made by a student on an astronomy exam[*]:

2881: If two stars have the same luminosity, the star with the lower temperature must be larger.

Discuss whether this claim is correct or incorrect, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

[*] waiferx.blogspot.com/2009/05/astronomy-midterm-question-cooler.html.

Solution and grading rubric:

p:
Correct. Discusses how the H-R diagram and/or the Stefan-Boltzmann law (luminosity is proportional to size × Temperature⁴) demonstrates that in order for a cooler star to have the same luminosity as a hotter star, its lower temperature must be compensated for by having a larger size; thus the claim by that student is correct.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, the Stefan-Boltzmann law, and/or H-R diagram. May have argument based on the size of a star being dependent on luminosity and temperature.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on Wien's law, the Stefan-Boltzmann law, and/or H-R diagram.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 70158
Exam code: midterm02Rf0w
p: 31 students
r: 1 student
t: 0 students
v: 1 student
x: 1 student
y: 0 students
z: 0 students

Section 70160
Exam code: midterm02T4qz
p: 16 students
r: 2 students
t: 0 students
v: 2 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 0809), using the Stefan-Boltzmann law:

A sample "p" response (from student 1234), using a Hertzsprung-Russell diagram:

A sample "p" response (from student 1278) using both the Stefan Boltzmann law and a Hertzsprung-Russell diagram:

A sample "x" response (from student 4000), appealing to concepts other than than of the Stefan-Boltzmann law:

20171202

Astronomy midterm question: more luminous star redder than same-size less luminous star?

Astronomy 210 Midterm 2, fall semester 2017
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

RC: Star X is more luminous than star Y, but they are the same size. Is star X redder or bluer than star Y?
BrT: Since they have the same size, because star X is more luminous it will be redder.

Discuss why this answer is incorrect, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

[*] answers.yahoo.com/question/index?qid=20110203173510AAHqejO.

Solution and grading rubric:

p:
Correct. Uses the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate that in order for two stars to have the same size, the more luminous star X must be hotter than the less luminous star Y, and from Wien's law "redder" corresponds to cooler temperatures, and thus star X cannot be redder than star Y.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, the Stefan-Boltzmann law, and/or H-R diagram.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on Wien's law, the Stefan-Boltzmann law, and/or H-R diagram.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 70158
Exam code: midterm02Sm5n
p: 29 students
r: 5 students
t: 9 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students

Section 70160
Exam code: midterm02nJv3
p: 24 students
r: 2 students
t: 5 students
v: 0 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 8622), using a graphical "box method" to indicate relative quantities in the Stefan-Boltzmann law:

A sample "p" response (from student 1881), using an H-R diagram:

A sample "p" response (from student 1072), using both an H-R diagram and the "box method":

20170518

Astronomy final exam question: hottest supergiants the biggest stars possible?

Astronomy 210 Final Exam, spring semester 2017
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

Pdg: Are the hottest supergiants the biggest stars possible on an H-R diagram?
qcp: They are.

Discuss whether this answer is correct or incorrect, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

[*] answers.yahoo.com/question/index?qid=20170323215116AASJ9GS.

Solution and grading rubric:

p:
Correct. Discusses how the Stefan-Boltzmann law and/or H-R diagram shows that the hottest supergiant is not necessarily the largest possible star, as the cooler supergiants would be larger.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least discussion demonstrates understanding of the Stefan-Boltzmann law and/or H-R diagram. May have instead conflated "brightest" with "biggest" that the hottest supergiants would be the most luminous supergiants possible, or that the hottest main-sequence stars would be the most luminous stars possible.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use the Stefan-Boltzmann law and/or H-R diagram.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on the Stefan-Boltzmann law and/or H-R diagram.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 30674
Exam code: finalnmSS
p: 8 students
r: 3 students
t: 4 students
v: 2 students
x: 1 student
y: 0 students
z: 0 students

Section 30676
Exam code: finalSBr6
p: 16 students
r: 1 student
t: 12 students
v: 5 students
x: 1 student
y: 0 students
z: 2 students

A sample "p" response (from student 1866):

Another sample "p" response (from student 6850):

A sample "t" response (from student 8959):

Another sample "t" response (from student 9433):

20170429

Astronomy midterm question: example of a cooler star larger than a hotter star?

Astronomy 210 Midterm 2, spring semester 2017
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

Pdg: What is an example of a cooler star being larger than a hotter star?
nin: The sun and a red star like Betelgeuse.

Discuss why this answer is correct, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

[*] answers.yahoo.com/question/index?qid=20170301055021AAZuNwb.

Solution and grading rubric:

p:
Correct. Uses Wien's law to determine that the sun would be the hotter (yellow) star, while Betelgeuse would be the (red) cooler star. Then uses the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how Betelgeuse would need to be either a red giant or a red supergiant (which it actually is) in order to be cooler and larger than the sun, a medium-mass main-sequence star.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Compares two stars (hotter, smaller vs. cooler, larger), where the hotter star is more luminous than the cooler star, but does not explicitly compare the sun versus a red (giant/supergiant) star.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least discussion demonstrates understanding of Wien's law, but the Stefan-Boltzmann law and/or H-R diagram discussion is garbled, with a hotter, smaller sun having the same luminosity as a cooler, larger red (giant/supergiant) star; or may have erroneously claimed that the two stars have the same temperature, but Stefan-Boltzmann law and/or H-R diagram discussion is consistent with this mistake in Wien's law.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, the Stefan-Boltzmann law, and/or H-R diagram.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on Wien's law, the Stefan-Boltzmann law, and/or H-R diagram.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 30674
Exam code: midterm02nDcc
p: 9 students
r: 9 students
t: 2 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 9433):

Astronomy midterm question: example of a cooler star smaller than a hotter star?

Astronomy 210 Midterm 2, spring semester 2017
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

Pdg: What is an example of a cooler star being smaller than a hotter star?
nin: The sun and a red star like Barnard's star.

p:
Correct. Uses Wien's law to determine that the sun would be the hotter (yellow) star, while Barnard's star would be the (red) cooler star. Then uses the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how Barnard's star would need to be a red dwarf in order to be cooler and smaller than the sun, a medium-mass main-sequence star.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Compares two stars (hotter, larger vs. cooler, smaller), where the hotter star is more luminous than the cooler star, but does not explicitly compare the sun versus a red (dwarf) star.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least discussion demonstrates understanding of Wien's law, but the Stefan-Boltzmann law and/or H-R diagram discussion is garbled, with a hotter, larger sun having the same luminosity as a cooler, smaller red (dwarf) star; or may have erroneously claimed that the two stars have the same temperature, but Stefan-Boltzmann law and/or H-R diagram discussion is consistent with this mistake in Wien's law.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, the Stefan-Boltzmann law, and/or H-R diagram.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on Wien's law, the Stefan-Boltzmann law, and/or H-R diagram.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 30676
Exam code: midterm02sL0w
p: 22 students
r: 4 students
t: 9 students
v: 5 students
x: 3 students
y: 0 students
z: 0 students

A sample "p" response (from student 3428):

20170105

Astronomy final exam question: luminosity/temperature of sun as a red giant?

Astronomy 210 Final Exam, fall semester 2016
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was answered:

nscr: When the sun becomes a red giant, it will be more luminous and cooler than it was as a main sequence star.

p:
Correct. Discusses how the Stefan-Boltzmann law and/or H-R diagram shows that as the sun (a medium-mass star) becomes a red giant, it becomes more luminous and cooler (moving higher up, and to the right on the H-R diagram).
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least discussion demonstrates understanding of Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 70158
Exam code: finalS1tH
p: 33 students
r: 0 students
t: 2 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

Section 70160
Exam code: finalnwhP
p: 16 students
r: 1 student
t: 5 students
v: 1 student
x: 0 students
y: 1 student
z: 0 students

A sample "p" response (from student 0924):

Another sample "p" response (from student 3168), using both the "box method" to fill in relative Stefan-Boltzmann law parameters:

20161126

Astronomy midterm question: giant hotter or cooler to be bigger than a supergiant?

Astronomy 210 Midterm 2, fall semester 2016
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

Pdg: Does a giant need to be cooler or hotter in order to be bigger in size than a supergiant?
non: Hotter.

p:
Correct. Uses the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how a giant cannot be hotter in order to be bigger than a supergiant, by arguing that since a giant must be dimmer than a supergiant, in order for the giant to be bigger than a supergiant, the giant must have a cooler temperature. (Using Wien's law is not necessary to answer this question.)
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least discussion demonstrates understanding of the Stefan-Boltzmann law and/or H-R diagram.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use the Stefan-Boltzmann law and/or H-R diagram.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on the Stefan-Boltzmann law and/or H-R diagram.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Section 70158
Exam code: midterm02sU6A
p: 15 students
r: 8 students
t: 9 students
v: 3 students
x: 1 student
y: 0 students
z: 0 students

Section 70160
Exam code: midterm02NbnW
p: 10 students
r: 3 students
t: 6 students
v: 3 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 0301):

20160503

Astronomy midterm question: same luminosity, but different temperature and size stars

Astronomy 210 Midterm 2, spring semester 2016
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

??: If two stars have the same luminosity, is it always true that the star with the lower temperature must be bigger?
qcp: Yes, that's true. A cooler star means that it must be bigger to be of equal luminosity.

p:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how a cooler star must be bigger than a hotter star to have the same luminosity.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least discussion demonstrates understanding of Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 30674
Exam code: midterm02n4s5
p: 12 students
r: 3 students
t: 3 students
v: 1 student
x: 2 students
y: 1 student
z: 0 students

A sample "p" response (from student 1503), using both the "box method" to fill in relative Stefan-Boltzmann law parameters, along with using the diagonal lines on an H-R diagram to compare size:

A sample "x" response (from student 1096), appealing to recent tragic events in pop culture:

Astronomy midterm question: red dwarf same size as white dwarf?

Astronomy 210 Midterm 2, spring semester 2016
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

??: Can a red dwarf have the same size as a white dwarf?
Bpt: They can have the same size if the red dwarf was dimmer than the white dwarf.

p:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how a red dwarf can be the same size as a white dwarf by recognizing that:
1. from Wien's law, the red dwarf is cooler than the white dwarf;
2. from the Stefan-Boltzmann law (or interpreting an H-R diagram), the lower temperature red dwarf must have a lower luminosity than a white dwarf of the same size.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least discussion demonstrates understanding of Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 30676
Exam code: midterm02sLoX
p: 37 students
r: 8 students
t: 4 students
v: 3 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 0796), using the "box method" to fill in relative Stefan-Boltzmann law parameters:

A sample "p" response (from student 5713), using the diagonal lines on an H-R diagram to compare size:

A sample "p" response (from student 8041):

20151128

Astronomy midterm question: same luminosity, same size, different temperature stars?

Astronomy 210 Midterm 2, fall semester 2015
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

??: Can two stars with the same luminosity have the same size, but different temperatures?
Lodar: If the temperatures are different, the sizes would also have to be different for their luminosities to be the same.

p:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how same luminosity stars with different temperatures would have to have different sizes. May also demonstrate that same luminosity stars with different temperatures cannot have the same temperatures.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least discussion demonstrates understanding of Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Section 70158
Exam code: midterm02sP3c
p: 34 students
r: 3 students
t: 1 student
v: 2 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 5635) discussing how same luminosity stars with different temperatures would have to have different sizes:

A sample "p" response (from student 1022), discussing how same luminosity stars with different temperatures cannot have the same temperatures:

Astronomy midterm question: hotter giant same size as cooler supergiant?

Astronomy 210 Midterm 2, fall semester 2015
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

??: Can a giant be the same size as a supergiant if the giant were hotter than the supergiant?
MirJ: No.

p:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to demonstrate how a supergiant and a giant with the same size is not possible if the giant is hotter by discussing either that:
1. for a supergiant and giant with the same size, the supergiant must be hotter than the giant (thus the giant cannot be hotter than the supergiant);
2. for a giant hotter than a supergiant of the same size, the giant would be more luminous than the supergiant (which is not possible, as all supergiants are more luminous than giants);
3. for a giant hotter than a supergiant, the giant must be smaller than the supergiant (thus the giant cannot be the same size as the supergiant).
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At least discussion demonstrates understanding of Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Section 70160
Exam code: midterm02n1N0
p: 18 students
r: 2 students
t: 1 student
v: 3 students
x: 6 students
y: 1 student
z: 0 students

A sample "p" response (from student 4321) discussing how a supergiant must be hotter than the giant of the same size (thus the giant cannot be hotter than the supergiant):

A sample "p" response (from student 6392) how giant that is hotter than a supergiant of the same size would be more luminous than the supergiant (which is not possible, as all supergiants are more luminous than giants):

A sample "p" response (from student 1996) how a giant hotter than a supergiant must be smaller than the supergiant (thus the giant cannot be the same size as the supergiant):

20150514

Astronomy midterm question: red supergiants versus red giants

Astronomy 210 Midterm 2, spring semester 2015
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was answered:

Yg: Red supergiants can be the same size as red giants.

p:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to discuss how a red supergiant cannot be the size as a red giant by either arguing:
1. that from Wien's law, a red supergiant must have the same temperature as a red giant, and from the H-R diagram a supergiant must be more luminous than a giant, such that from the Stefan-Boltzmann law, for two stars that have the same temperature, the more luminous supergiant must be larger than the less luminous giant, which makes it not possible for the supergiant to have the same size as the giant; or instead argues
2. that from the Stefan-Boltzmann law, for two stars that have the same size, the more luminous supergiant must have a hotter surface temperature, which makes it not possible to have the same color as the less luminous giant.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At last discussion demonstrates understanding of Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Section 30674
Exam code: midterm02N4ra
p: 20 students
r: 1 student
t: 11 students
v: 4 students
x: 1 student
y: 1 student
z: 0 students

Section 30676
Exam code: midterm02s0Ju
p: 30 students
r: 5 students
t: 12 students
v: 2 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 2194):

A sample "t" response (from student 1175):

20141213

Astronomy midterm question: bigger, more luminous stars always cooler or hotter?

Astronomy 210 Midterm 2, fall semester 2014
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked:

Pd: Are the bigger, more luminous stars always the cooler stars?
Sa: You wouldn't be right because "more luminous" means more energy output, which means bigger and hotter.

p:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to discuss how a more luminous star does not necessarily have to be both bigger and hotter, by comparing:
bright/larger/cooler vs. dim/smaller/hotter stars;
bright/larger/(same temperature) vs. dim/smaller/(same temperature) stars;
bright/smaller/hotter vs. dim/larger/cooler stars;
bright/(same size)/hotter vs. dim/(same size)/cooler stars.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Or as (p), but may instead compare:
(same brightness)/smaller/hotter vs. (same brightness)/larger/cooler stars;
brighter/larger/hotter vs. dim/smaller/cooler star;
thus not sufficiently discussing why the response would not always be correct.
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. At last discussion demonstrates understanding of Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not clearly based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 70158
Exam code: midterm02s0vA
p: 20 students
r: 14 students
t: 6 students
v: 3 students
x: 1 student
y: 0 students
z: 0 students

Section 70160
Exam code: midterm02n4Rs
p: 20 students
r: 7 students
t: 2 students
v: 2 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 1327) comparing a bright/larger/cooler star versus a dim/smaller/hotter star:

A sample "p" response (from student 5656) comparing a bright/larger star that has the same temperature as a dim/smaller star:

A sample "p" response (from student 5309) comparing a bright/smaller/hotter star versus a dim/larger/cooler star:

A sample "p" response (from student 1795) comparing a bright/hotter star that has the same temperature as a dim/cooler star:

20140511

Astronomy midterm question: cooler star more luminous than a hotter star?

Astronomy 210 Midterm 2, spring semester 2014
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was given the following answers:

CM: I keep thinking that a cooler star could be more luminous than a hotter star--is this true?
Okl: No, it cannot be true.
Do: There are situations in which this may be true.

Discuss why this answer is incorrect, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

[*] Adapted from https://answers.yahoo.com/question/index?qid=20090316143453AAmTD1h.

Solution and grading rubric:

p = 20/20:
Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to show specifically how it is possible for a cooler star to be more luminous than a hotter star, provided that the cooler star is sufficiently larger than the hotter star.
r = 16/20:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. As (p), but may instead demonstrate how a cooler star could be equally luminous as a hotter star.
t = 12/20:
Contains right ideas, but discussion is unclear/incomplete or contains major errors.
v = 8/20:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
x = 4/20:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
y = 2/20:
Irrelevant discussion/effectively blank.
z = 0/20:
Blank.

Grading distribution:
Section 30674
Exam code: midterm02n4iL
p: 22 students
r: 4 students
t: 1 student
v: 0 students
x: 1 student
y: 0 students
z: 0 students
z: 0 students

A sample "p" response (from student 0507) using an H-R diagram:

Another sample "p" response (from student 0794) using the "box model" of the Stefan-Boltzmann law:

Yet another sample "p" response (from student 3946) showing all the possible entries in the Stefan-Boltzmann "box model":

Astronomy midterm question: brighter, larger star is hotter?

Astronomy 210 Midterm 2, spring semester 2014
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

qu: If you have two stars that are at equal distance, and one is brighter than the other, then the brighter one must be hotter if it is the larger one.

Discuss why this answer would not necessarily always be correct, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

[*] answers.yahoo.com/question/index?qid=20140327175847AARrJhx.

Solution and grading rubric:

p:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to discuss how a brighter/larger star does not necessarily have to be hotter than a dimmer/smaller star, by comparing:
• bright/larger/cooler vs. dim/smaller/hotter stars;
• bright/larger/(same temperature) vs. dim/smaller/(same temperature) stars;
or makes other comparisons between:
• bright/smaller/hotter vs. dim/larger/cooler stars;
• bright/(same size)/hotter vs. dim/(same size)/cooler stars.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Or as (p), but may instead compare:
• (same brightness)/smaller/hotter vs. (same brightness)/larger/cooler stars;
despite being given "one star is brighter than the other."
t:
Contains right ideas, but discussion is unclear/incomplete or contains major errors.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzmann law.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 30676
Exam code: midterm02sh7F
p: 26 students
r: 4 students
t: 3 students
v: 8 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 0417) showing that the brighter, larger star could be cooler:

Another sample "p" response (from student 1000) showing that the brighter, hotter star could have the same size:

Another sample "p" response (from student 1133) showing how the brighter, larger star could have the same temperature:

20131208

Astronomy midterm question: bright-red star versus dim-orange star

Astronomy 210 Midterm 2, fall semester 2013
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

Pdg: Your friend asks, "Of all the stars we can see in the sky tonight, which is the largest one?" You search all over the sky--should you point to a star that is bright and red, or dim and orange? (Assuming they are equally far away.)
Thms: Bright and red.

p:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to show specifically how the "bright and red" star is cooler and more luminous, and thus must be larger in size than the "dim and orange" star, which is hotter and less luminous.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t: Contains right ideas, but discussion is unclear/incomplete or contains major errors.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzman law.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzman law.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 70158
Exam code: midterm02sL4g
p: 19 students
r: 8 students
t: 13 students
v: 7 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 6933) using an H-R diagram (provided on the exam):

Another sample "p" response (from student 0483) using a "box-method" analysis of the Stefan-Boltzmann law:

Yet another sample "p" response (from student 2729), using both an H-R diagram and a Stefan-Boltzmann law "box":

A sample "x" response (from student 0126):

Astronomy midterm question: example of a cool star more luminous than a hot star?

Astronomy 210 Midterm 2, fall semester 2013
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

y2j: What is an example of how a cool star can be more luminous than a hot star?
Brnt: Two stars in the constellation Orion: Betelgeuse, a supergiant, and Bellatrix, a giant.

p:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to show specifically how Betelgeuse (supergiant) is cooler, larger and more luminous than Bellatrix (giant), which is hotter, smaller, and less luminous.
r:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. As (p), but arbitrarily picks one other star to compare (typically a white dwarf) with either Betelgeuse or Bellatrix. Or instead may conflate mass with size.
t: Contains right ideas, but discussion is unclear/incomplete or contains major errors.
v:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzman law.
x:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzman law.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Section 70160
Exam code: midterm02nI5o
p: 13 students
r: 5 student
t: 3 students
v: 5 students
x: 1 student
y: 1 student
z: 0 students

A sample "p" response (from student 3055):

A sample "y" response (from student 1112):

20121205

Astronomy midterm question: small hot stars always more luminous than cool big stars?

Astronomy 210 Midterm 2, fall semester 2012
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board(*) was asked and answered:

Pd: Is it possible that a small hot star and a cool big star [located the same distance from us] can be equally bright?
Star Dust: Small-hot is [always] more luminous than cool-big.

Discuss why this answer is not correct, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

*Adapted from: http://answers.yahoo.com/question/index?qid=20120928201352AA8dDbB.

Solution and grading rubric:

p = 20/20:
Correct. Uses Wien's law, the Stefan-Boltzmann law and/or interprets H-R diagram to show that small, hot stars can be either (a) equally luminous, or (b) less luminous than cool, big stars.
r = 16/20:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
t = 12/20:
Contains right ideas, but discussion is unclear/incomplete or contains major errors.
v = 8/20:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzman law.
x = 4/20:
Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzman law.
y = 2/20:
Irrelevant discussion/effectively blank.
z = 0/20:
Blank.

Grading distribution:
Section 70160
Exam code: midterm02NuF7
p: 20 students
r: 5 students
t: 1 student
v: 1 student
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 5411) demonstrating how a small hot star could be as luminous as a large cool star:

Another sample "p" response (from student 0716) demonstrating how a small hot star could be less luminous than a large cool star:

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