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)?
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)?
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!
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!
