(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.)

2. Relevant equations

(dv/dT)/v =β

3. 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?

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# Amount of water spilled when the temperature is changed

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