An ordinary drinking glass is filled to the brim with water (268.4 mL) at 2.0 ° C and placed on the sunny pool deck for a swimmer to enjoy. If the temperature of the water rises to 32.0 ° C before the swimmer reaches for the glass, how much water will have spilled over the top of the glass? Assume the glass does not expand.

Respuesta :

Answer:

[tex]\Delta V=1.667\times10^{-3}[/tex]

Explanation:

Given the initial temperature T_i=2° C

final temperature T_f= 32° C

The original volume of water Vo=268.8 mL= 0.2688 L

we need to calculate the change in the volume

As we know that volume expansion is given by

[tex]\frac{\Delta V}{V_0}= \beta\Delta T[/tex]

ΔV= change in Volume

β= expansion coefficient = [tex]207\times10^{-6} K^{-1}[/tex]

therefore,

[tex]\Delta V= \beta\Delta T V_0[/tex]

plugging values we get

[tex]\Delta V=207\times10^{-6} K^{-1} (32-2)\times0.2688[/tex]

[tex]\Delta V=1.667\times10^{-3}[/tex]

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