Question

# I received my favourite cologne, bottled in a metallic flask with a spherical cavity, on my birthday in December. I used it modestly only on special occasions, and found that I have finally emptied the bottle in mid-April, when the temperature had risen by 25∘C from December. If the metal's coefficient of superficial (area) expansion is 46 × 10−5/∘C, how much extra cologne can I refill my bottle with, compared to the initial volume (answer in mL)?

A

5 mL

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B

2 mL

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C

10 mL

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D

3.5 mL

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Solution

## The correct option is B 2 mL As the bottle enlarges over the change of seasons, so will the cavity inside. Now, the coefficient of volume expansion γ = 3β2 ⇒ γ = 32 × 46 × 10−5/∘C. The change in volume ΔV will be- ΔV = (V′−V) = V γΔT = 43 × π × 33 × 69 × 10−5 × 25 cm3 = 1.95 cm3 = 1.95 mL ≈2 mL. I guess I get about one extra spray on refill, thanks to thermal expansion!

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