Question

What is the change in length of a 3.00-cm-long column of mercury if its temperature changes from 37.0°C to 40.0°C, assuming the mercury is constrained to a cylinder but unconstrained in length? Your answer will show why thermometers contain bulbs at the bottom instead of simple columns of liquid.

(a) 0.087 cm
(b) 0.090 cm
(c) 0.093 cm
(d) 0.097 cm

Answer 1

The change in length of a 3.00-cm-long column of mercury when its temperature changes from 37.0°C to 40.0°C is 0.090 cm. Thermometers contain bulbs at the bottom to allow the liquid to expand and contract, ensuring accurate temperature measurements.

Step-by-step explanation:

The change in length of a column of mercury can be calculated using the formula:

ΔL = L × α × ΔT

Where ΔL is the change in length, L is the original length, α is the coefficient of linear expansion, and ΔT is the change in temperature.

In this case, the change in length is calculated as:

ΔL = 3.00 cm × (18.0 × 10-6 °C-1) × (40.0 °C - 37.0 °C) = 0.090 cm

Therefore, the change in length of the mercury column is 0.090 cm.

Thermometers contain bulbs at the bottom instead of simple columns of liquid because the bulb provides a reservoir for the liquid to expand into and contract from, allowing for accurate measurement of temperature changes. If the liquid were in a simple column, it would not have room to expand and the measurements would be inaccurate.