IB Physics SL B.1 Thermal energy transfers questions

Exam-style multiple choice and written questions with full markschemes. Check multiple choice answers straight away, or type, photograph or draw a written answer and get it marked.

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Question 1

Multiple choiceMedium1 mark

A star and the Sun are both modelled as black bodies. The star’s surface area is four times the Sun’s, and its surface temperature is half the Sun’s; both temperatures are absolute, measured in kelvin. What is the star’s luminosity in terms of LsunL_{\text{sun}}

Show answer and explanation

Answer: B. For a black body, L=σAT4L=\sigma AT^4 Comparing the star with the Sun cancels σ\sigma

LLsun=AAsun(TTsun)4=4(12)4=14.\frac{L}{L_{\text{sun}}} =\frac{A}{A_{\text{sun}}}\left(\frac{T}{T_{\text{sun}}}\right)^4 =4\left(\frac12\right)^4 =\frac14.

A: includes the temperature factor but omits the area ratio.
C: uses a square rather than the fourth power of the temperature ratio.
D: includes the area ratio but ignores the temperature dependence.
Remember: for black-body radiation, luminosity depends on the fourth power of absolute temperature.

Question 2

Paper 2Medium11 marks

An observer on Earth measures the apparent brightness of stars A and B shown in Figure 1. Assume that both stars emit uniformly in all directions and that absorption between each star and Earth is negligible.

Earth (observer)dA=2.0×1017 mdB=4.0×1017 mAbA=3.0×10−8 W m−2BbB=1.0×10−8 W m−2
(a)

State which star has the greater apparent brightness.

[1]
(b)

Determine the ratio LB/LAL_B/L_A

[3]
(c)

Calculate the luminosity of star A.

[2]
(d)

A third star, C, has twice the luminosity of star A and an apparent brightness of 1.2×10−8 W m−21.2\times10^{-8}\,\mathrm{W\,m^{-2}} Determine its distance from Earth.

[3]
(e)

Explain why the apparent brightness of a star decreases as its distance from Earth increases, if its luminosity is unchanged.

[2]

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