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 level if the 350cm^3 of coffee is in a 7.00-cm-diameter cup and decreases in temperature from 95.0°C to 45.0°C. (Most of the drop in level is actually due to escaping bubbles of air.)

(a) 3.7 mm
(b) 4.2 mm
(c) 4.8 mm
(d) 5.3 mm

Answer 1

The decrease in the coffee level cannot be attributed to thermal contraction, as the observed decrease is greater than the decrease predicted by thermal contraction.

Step-by-step explanation:

To determine if the decrease in the coffee level is due to thermal contraction, we need to calculate the decrease in level based on thermal contraction and compare it to the observed decrease. Since most of the drop in level is due to escaping bubbles of air, we can assume that the observed decrease is not solely due to thermal contraction. The decrease in level due to thermal contraction can be calculated using the formula:

Δh = α × h × ΔT

Where Δh is the decrease in level, α is the coefficient of thermal expansion, h is the initial height of the coffee, and ΔT is the change in temperature. However, since the question states that the observed decrease is 3.00 mm, which is greater than the decrease predicted by thermal contraction, it can be concluded that the decrease is not solely due to thermal contraction. Therefore, the decrease cannot be attributed to thermal contraction.