Turn over 19 9 A Hertzsprung-Russell (HR) diagram shows how the luminosity L depends on the surface temperature T for a group of stars. The HR diagram below is for a young star cluster. L T (a) (i) Explain how we can tell that the young star cluster is in the early stages of its evolution. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (ii) Explain why the most massive stars in the cluster have the greatest luminosities. (4) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. 20 (b) The HR diagram on the previous page shows an approximately linear relationship for stars in this cluster. (i) It is suggested that the relationship between luminosity L and surface temperature T is of the form L = kT n where k and n are constants. Explain why a graph of log L against log T would give a straight line. 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(ii) The table shows data for stars in this cluster. L / LSun T / K 39.5 10 600 545 16 400 20 600 26 800 535 000 44 900 1 770 000 53 300 Plot a graph of log L against log T on the grid opposite. Use the columns provided to show any processed data. (5) (iii) Determine a value for n. (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... n = ....................................................... Turn over 21 (Total for Question 9 = 15 marks) 22 BLANK PAGE