A physicist makes a cup of instant coffee and notices that as the coffee cools i

Question

A physicist makes a cup of instant coffee and notices that as the coffee cools its level drops 3.00 mm in the ordinary glass cup. Show that this cannot be due to thermal contraction by calculating the decrease in level if the 350 cm3 of coffee is in a 9.00 cm diameter cup and decreases in temperature from 95°C to 40.0°C. (Most of the drop in level is actually due to escaping bubbles of air.)

Answer should be in mm. I am lost on what to do. Please show what formulas to use, and show complete work.

Thanks in advance.

Explanation / Answer

here,

volume of the cofee , V = 350 cm^3 = 350 * 10^-6 m^3

radius of thecup , r = 0.045 m

change in temprature , delta T = ( 95 - 40) = 55 degree C

let the change height be h

delta V = pi* 0.045^2 * h

alpha = 207 * 10^-6 degree C^-1

dV/V = dT * alpha

pi * 0.045^2 * h = 350 * 10^-6 * 207 * 10^-6 * 55

h = 6.26 * 10^-4 m

hence the change in height due to thermal compression is very small,

so the 3 mm is not due to the thermal compression

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