Question

A physicist makes a cup of instant coffee and notices that, as the coffee cools, its level drops 3.00 mm in the glass cup. Show that this decrease cannot be due to thermal contraction by calculating the decrease in millimeters in level if the 350 cm^3 of coffee is in a 5.00 cm diameter cup and decreases in temperature from 95°C to 44.0°C. (Most of the drop in level is actually due to escaping bubbles of air.)

Answer 1

Answer:

change in height  is 1.664 mm

Explanation:

Given data

drops = 3.00 mm

diameter = 5.00 cm = 0.05 mm

decrease  =  350 cm^3

temperature = 95°C to 44.0°C

to find out

the decrease in millimeters in level

solution

we  will calculate here change in volume so we can find how much level is decrease

change in volume = β v change in temp   ...............1

here change in volume = area× height

so = $\pi$ /4 × d² h

so we can say change in volume =  $\pi$ /4 × d² × change in height   .......2

so from equation 1 and 2  we calculate change in height

( β(w) -β(g) )× v× change in temp = $\pi$ /4 × d² × change in height

change in height = 4 × ( β(w) -β(g) ) v× change in temp / $\pi$ /4 × d²

put all value here

change in height = 4 × ( 210 - 27 )(350 ) $10^{-6}$× (95-44) / $\pi$ /4 × 0.05²

change in height  is 1.664 mm