Question

table 17.6 key properties of some well-known main-sequence stars
star\tspectral type\tmass, m (solar masses)\tcentral temperature (10⁶ k)\tluminosity, l (solar luminosities)\testimated lifetime (myr) (10⁶ years)
spica b*\tb2v\t6.8\t25\t800\t90
véga\ta0v\t2.6\t21\t50\t500
sirius\taiv\t2.1\t20\t22\t1000
alpha centauri\tg2v\t1.1\t17\t1.6\t7060
sun\tg2v\t1.0\t15\t1.0\t10,000
proxima centauri\tmsv\t0.1\t0.6\t0.00006\t16,000,000
based on the figure above, what is true about the estimated lifetime of stars?
a\tstars that have a short estimated lifetime tend to be large and hot.
b\tstars that are very cool tend to be large and short-lived.
c\tstars that have a long estimated lifetime tend to be large and hot.
d\tstars that are very large tend to be cool and short-lived.

Explanation:

Step1: Analyze each option

• Option A: Check the table. Stars with short estimated lifetime (e.g., Spica B with 90×10⁶ years, Vega with 500×10⁶ years) have large mass (Spica B: 6.8, Vega: 2.6) and high central temperature (Spica B*: 25×10⁴ K, Vega: 21×10⁴ K, so hot). So this option matches.
• Option B: Stars with long lifetime (e.g., Proxima Centauri: 16,000×10⁶ years) have small mass (0.1) and low temperature (0.6×10⁴ K, cool), not large and hot. Eliminate.
• Option C: Cool stars (low temperature, like Proxima Centauri: 0.6×10⁴ K) have small mass (0.1) and long lifetime (16,000×10⁶ years), not large and short - lived. Eliminate.
• Option D: Very large stars (large mass, like Spica B*) have high temperature (25×10⁴ K, hot) and short lifetime (90×10⁶ years), not cool. Eliminate.

Answer:

A. Stars that have a short estimated lifetime tend to be large and hot.