IB · E · extended response
Two stars at the same temperature with very different luminosities
Nuclear and quantum physics · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 6
- Topics
- 1
- Answer
- Complete
Three stellar observations
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Relative luminosity
Horizontal axis (x): Surface temperature / K
Read the exact data as a table
| Surface temperature / K | Relative luminosity |
|---|---|
| 4000 | 1 |
| 4000 | 400 |
| 12000 | 0.01 |
These are the supplied values, not a worked answer. No fitted trend is drawn.
A main-sequence reference star and a red giant both have surface temperature 4000 K. The giant has luminosity 400 times the reference. A third star is a white dwarf with temperature 12000 K and luminosity 0.01 times the reference. Use L = 4πR²σT⁴. The supplied data place the three stars on temperature–luminosity axes; luminosities are relative to the reference star. Supplied data (Surface temperature / K; Relative luminosity): (4000, 1), (4000, 400), (12000, 0.01).
- (a)
Determine the radius of the giant and dwarf relative to the reference. Explain why colour alone cannot determine luminosity.
3 marks - (b)
Relate these observations to an H–R diagram and distinguish low-mass from high-mass stellar endpoints.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Determine the radius of the giant and dwarf relative to the reference. Explain why colour alone cannot determine luminosity.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
At equal temperature, L∝R², so the giant radius ratio is √400 = 20.
- 2
For the dwarf, Rw/Rref = √(Lw/Lref)(Tref/Tw)² = √0.01×(1/3)² = 1/90.
- 3
Colour indicates a characteristic surface temperature, while luminosity also depends on emitting area. A hot small star may be less luminous than a cool large one.
(b)
Relate these observations to an H–R diagram and distinguish low-mass from high-mass stellar endpoints.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
A standard H–R diagram places hotter temperatures toward the left and often uses logarithmic luminosity. The supplied linear data plot must be relabelled or transformed before being read as a standard H–R diagram.
- 2
A Sun-like star can evolve into a red giant and leave a white dwarf after shedding outer layers. A white dwarf is not a newly formed small main-sequence star.
- 3
Sufficiently massive stars can undergo core-collapse supernovae and leave neutron stars or black holes. Initial mass, mass loss and interactions matter; a single universal life-cycle chain is inadequate.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- At equal temperature, L∝R², so the giant radius ratio is √400 = 20.
- For the dwarf, Rw/Rref = √(Lw/Lref)(Tref/Tw)² = √0.01×(1/3)² = 1/90.
- Colour indicates a characteristic surface temperature, while luminosity also depends on emitting area. A hot small star may be less luminous than a cool large one.
- A standard H–R diagram places hotter temperatures toward the left and often uses logarithmic luminosity. The supplied linear data plot must be relabelled or transformed before being read as a standard H–R diagram.
- A Sun-like star can evolve into a red giant and leave a white dwarf after shedding outer layers. A white dwarf is not a newly formed small main-sequence star.
- Sufficiently massive stars can undergo core-collapse supernovae and leave neutron stars or black holes. Initial mass, mass loss and interactions matter; a single universal life-cycle chain is inadequate.
Private on this device