Chapter 24 — Self-Check Quiz: Thermal Control
Twenty quick questions to test whether the chapter's core ideas have stuck. Aim to answer from memory, then check the key at the end. Target: 16/20. Below that, re-read the sections flagged in the "Topics to review" map before moving to Chapter 25.
Multiple choice
1. A spacecraft in vacuum can shed heat to its surroundings by which mechanism? - (a) Convection to the surrounding space - (b) Conduction to the surrounding space - (c) Thermal radiation (infrared emission) - (d) All three, roughly equally
2. The solar flux at $1\ \text{AU}$ (the solar constant) is closest to: - (a) $136\ \text{W/m}^2$ - (b) $1{,}361\ \text{W/m}^2$ - (c) $13{,}610\ \text{W/m}^2$ - (d) $5.67\times10^{-8}\ \text{W/m}^2$
3. The radiative equilibrium temperature of a surface scales with its absorptivity and emissivity as: - (a) $\alpha/\varepsilon$ - (b) $(\alpha/\varepsilon)^{1/2}$ - (c) $(\alpha/\varepsilon)^{1/4}$ - (d) $(\varepsilon/\alpha)^{1/4}$
4. When a low-Earth-orbit satellite passes into Earth's shadow, which loads switch off? - (a) Direct sunlight only - (b) Direct sunlight and albedo - (c) Planetary infrared only - (d) All external loads, including planetary IR
5. Multi-layer insulation works primarily by: - (a) Trapping a layer of still air like a wool sweater - (b) Conducting heat away through its spacers - (c) Interposing many low-emissivity radiation shields in series - (d) Absorbing heat in its thermal mass
6. A radiator that must operate in sunlight should have: - (a) High $\alpha$, high $\varepsilon$ (black paint) - (b) Low $\alpha$, high $\varepsilon$ (optical solar reflector) - (c) High $\alpha$, low $\varepsilon$ (polished metal) - (d) Low $\alpha$, low $\varepsilon$ (gold foil)
7. A heat pipe transports heat along its length mainly by: - (a) Conduction through solid copper - (b) A pumped single-phase fluid loop - (c) Evaporation at the hot end and condensation at the cold end (latent heat) - (d) Radiation down a mirrored tube
8. A fast-spinning grey sphere ($\alpha = \varepsilon$) at $1\ \text{AU}$ settles near: - (a) $2.7\ \text{K}$ - (b) $255\ \text{K}$ - (c) $278\ \text{K}$ - (d) $394\ \text{K}$
9. The rate at which a heat leak $Q$ boils off a cryogen of latent heat $h_{fg}$ is: - (a) $\dot m = Q\,h_{fg}$ - (b) $\dot m = Q/h_{fg}$ - (c) $\dot m = h_{fg}/Q$ - (d) $\dot m = Q/(h_{fg}\,T)$
10. A thermal louver regulates temperature by: - (a) Pumping coolant faster when hot - (b) Mechanically varying the effective emittance of a radiator, driven by temperature, with no power - (c) Firing small heaters on a thermostat - (d) Rotating the whole spacecraft
11. Earth's average outgoing infrared flux (planetary IR) seen by a low-orbiting spacecraft is closest to: - (a) $24\ \text{W/m}^2$ - (b) $240\ \text{W/m}^2$ - (c) $1{,}361\ \text{W/m}^2$ - (d) $2{,}400\ \text{W/m}^2$
12. Why does the James Webb Space Telescope reach about $40\ \text{K}$ for its near-infrared instruments? - (a) A large onboard refrigerator does all the cooling - (b) It is far enough from the Sun that $40\ \text{K}$ is the ambient temperature - (c) A large sunshield at L2 blocks the Sun, Earth, and Moon so the cold side radiates passively to space - (d) Liquid helium is sprayed continuously over the optics
True / false (state one sentence of justification)
13. A physically larger sphere of the same material runs hotter than a small one at the same distance from the Sun.
14. Black paint always runs hotter in sunlight than any other coating, because black absorbs the most.
15. The $2.7\ \text{K}$ cosmic background contributes a negligible radiative heat input to a spacecraft and can be treated as a $0\ \text{K}$ sink.
16. Coating properties are fixed for the life of the mission, so beginning-of-life values are safe to design with.
17. Adding internal electronics dissipation always raises a surface's equilibrium temperature.
Short answer
18. In one or two sentences, explain why white paint (which looks bright) runs cold in sunlight while polished aluminum (which looks shiny) runs hot.
19. Name the two dimensionless ratios that, together with location, dominate a surface's equilibrium temperature, and say what each one represents physically.
20. Why is eclipse the worst-case cold condition for a satellite even though the spacecraft still receives Earth's infrared and generates its own internal heat?
Answer Key
| # | Answer | One-line rationale |
|---|---|---|
| 1 | c | In vacuum there is no medium for convection/conduction to the surroundings; only radiation reaches space. |
| 2 | b | $S = 1361\ \text{W/m}^2$ at 1 AU (Appendix B). |
| 3 | c | $T_{\text{eq}} \propto (\alpha/\varepsilon)^{1/4}$ — the fourth root of the property ratio. |
| 4 | b | Albedo is reflected sunlight, so it dies with the Sun; planetary IR and internal power continue. |
| 5 | c | Each reflective shield cuts radiative transfer by $1/(N+1)$; MLI is a stack of them. |
| 6 | b | Low $\alpha$ resists absorbing sunlight; high $\varepsilon$ emits strongly — the OSR recipe. |
| 7 | c | A heat pipe moves latent heat via evaporation/condensation, with a wick returning the liquid. |
| 8 | c | $T = (S/4\sigma)^{1/4} = 278\ \text{K}$ for a grey isothermal sphere at 1 AU. |
| 9 | b | Energy balance: heat in $\div$ latent heat = mass boiled per unit time. |
| 10 | b | Bimetal-driven blades vary effective emittance between ~0.1 (shut) and ~0.7 (open), power-free. |
| 11 | b | $\approx S(1-a)/4 = 1361(0.7)/4 \approx 238\ \text{W/m}^2$. |
| 12 | c | A five-layer sunshield at L2 enables passive radiative cooling to ~40 K (a cryocooler adds the last step to ~7 K). |
| 13 | False | Size cancels in the balance (both areas scale as $r^2$); temperature is independent of radius. |
| 14 | False | Temperature depends on $\alpha/\varepsilon$; low-$\varepsilon$ metals run hotter despite reflecting more sunlight. |
| 15 | True | $\sigma(2.7)^4 \approx 3\times10^{-6}\ \text{W/m}^2$ — negligible; deep space is effectively a $0\ \text{K}$ sink. |
| 16 | False | UV and atomic oxygen raise $\alpha$ over time; the hot case must use degraded end-of-life values. |
| 17 | True | $Q_{\text{int}}$ adds to the absorbed side, so a higher $T$ is needed to radiate it away. |
| 18 | — | White paint has high IR $\varepsilon$ (emits well) and low solar $\alpha$ (reflects sun): low $\alpha/\varepsilon$, so cold. Polished aluminum has very low $\varepsilon$, so it cannot dump even the little it absorbs: high $\alpha/\varepsilon$, so hot. |
| 19 | — | $\alpha/\varepsilon$ (how a surface trades absorbing sunlight against emitting IR) and $A_{\text{sun}}/A_{\text{rad}}$ (how its sunlit projected area compares to its total radiating area). |
| 20 | — | The two biggest inputs — direct sun and its albedo — both vanish, leaving only weak planetary IR and modest internal power, while the $T^4$ radiative drain keeps pulling heat out. |
Topics to review by question
- Q1, Q15 → §24.1 (deep space, radiation-only) and the Overview.
- Q2, Q11 → §24.1 (solar flux, planetary IR).
- Q3, Q8, Q13, Q17, Q18, Q19 → §24.2 (equilibrium temperature and its scalings).
- Q5, Q14, Q16 → §24.3 (coatings and MLI).
- Q6, Q7, Q10 → §24.4 (radiators, heat pipes, louvers).
- Q9, Q12 → §24.5 (cryogenics, boiloff, sunshields).
- Q4, Q20 → §24.6 (eclipse and the cold case).
If you missed three or more, the most common weak spot is thinking in "color" instead of $\alpha/\varepsilon$ — reread §24.2–24.3 and redo exercises A3 and D2.