Question

What is the change in length of a 3.00-cm-long column of mercury if its temperature changes from 37.0ºC to 40.0ºC, assuming the mercury is unconstrained?

a) (0.076 cm)
b) (0.113 cm)
c) (0.150 cm)
d) (0.188 cm)

Answer 1

The change in length of a mercury column due to a temperature change can be calculated using the thermal expansion formula; however, the small calculated expansion of 0.001629 cm is not represented in the provided answer options.

Step-by-step explanation:

The change in length of a 3.00-cm-long column of mercury due to a temperature change from 37.0°C to 40.0°C can be calculated using the formula for linear expansion, ∆L = αL0∆T, where ∆L is the change in length, α is the coefficient of linear expansion for mercury, L0 is the original length, and ∆T is the change in temperature.

The coefficient of linear expansion for mercury is approximately 0.000181/°C. The change in temperature (∆T) is 3.0°C (from 37.0°C to 40.0°C). So the change in length (∆L) is calculated as 0.000181/°C × 3.00 cm × 3.0°C = 0.001629 cm or 0.01629 mm, which is a very small expansion not represented in the multiple-choice options provided. Thus, without the exact options, we cannot determine the correct answer from the given choices.