寿命 and 長寿: a battery's service life and a grandmother's longevity
Compare a battery reaching the end of its life and an exhibit of animal lifespans with a family celebrating a grandmother's longevity. Keep the lifespan or long life with the object or person described.
寿命 applies to a battery's service life
寿命 (じゅみょう) means lifespan or service life. In “古い電池が寿命を迎えて時計が止まった。” (“The old battery reached the end of its life, and the clock stopped.”), the old battery reached the end of its life and the clock stopped. The lifespan belongs to the battery, rather than a person's age.
Read the battery's 寿命を迎えて together with the clock's 止まった. The battery's life ended, and the clock stopped; they are distinct objects within the reported event.
Comparing animal lifespans
In “展示では動物ごとの寿命を図で比べている。” (“The exhibit compares the lifespans of animals in illustrations.”), an exhibit compares animal lifespans in illustrations. 動物ごとの identifies what is being compared, while 展示 places that comparison in the exhibit.
A comparison of animal lifespans does not establish an exact death date for every animal. The scene describes an illustrated comparison, rather than the fate of each individual animal.
長寿 describes longevity
長寿 (ちょうじゅ) means longevity. In “祖母の長寿を祝って家族で食事をした。” (“The family shared a meal to celebrate our grandmother's longevity.”), the family shared a meal to celebrate the grandmother's long life. Unlike the battery example, the person whose longevity is celebrated is the grandmother.
In “地域の長寿の秘訣を聞き取って記事にした。” (“I interviewed local residents and wrote an article about the secrets of their longevity.”), the speaker interviewed local residents and wrote an article about their longevity. The reported work is interviewing and writing; it does not establish medical proof that a particular practice is effective.
Can 寿命 in 古い電池が寿命を迎えて be read as the grandmother's age?
Show the answer and why
No. 寿命 belongs to the old battery's service life in this sentence, followed by the clock stopping. The grandmother is the person whose longevity is celebrated in the separate 祖母の長寿 example.