- #1

- 351

- 41

## Homework Statement

A glass bottle of nominal capacity 250 cm

^{3}is filled brim full of water at 20

^{o}C. If the bottle and content are heated to 50

^{o}C, how much water spills over? (For water,

*β*=0.21X10

^{-3}K

^{-1}. Assume that the expansion of the glass is negligible.)

## Homework Equations

(dv/dT)/v =

*β*[/B]

## The Attempt at a Solution

Let v

_{o}= 250 cm

^{3}, T

_{o}=20

^{o}C, T

_{1}= 50

^{o}C, to find: v

_{1}-v

_{0}

From the equation of coefficient of volume of expansion,

dv/v =

*βdT*

Integrating both sides, we get: ln(v

_{1}) - ln(v

_{o}) = 0.21x10

^{-3}*ln(50) - ln(20)

=> ln(v

_{1}) = 5.521 + 0.21x10-

^{3}x ln(5/2)

=> v

_{1}= 250.048

=> Δv = 0.048cm

^{3}

However, the answer is 1.6 cm

^{3}, what am I doing wrong?