Understanding the Volume Expansion Coefficient for Mercury

Calculating the Volume Expansion Coefficient

The volume expansion coefficient (β) can be determined using the formula:

β = (∆V / V) / ∆T

Where:

∆V is the change in volume,

V is the initial volume,

∆T is the change in temperature.

In this case, the change in volume (∆V) can be calculated using the formula:

∆V = A∆h,

Where:

A is the cross-sectional area of the thermometer tube,

∆h is the change in height of the mercury in the tube.

Substituting the given values into the formulas:

∆V = (0.0003 cm²)(h),

Using the volume of the mercury, V = 1000 mm³ = 1 cm³,

Plugging in these values into the equation for β:

β = (0.0003 cm²)(h) / (1 cm³)(1 °C),

β = 0.0003 cm² / (1 cm³)(1 °C),

β ≈ 0.0003 °C⁻¹.

Therefore, the volume expansion coefficient for mercury is 1.81×10⁻⁴ °C⁻¹. So, the correct option is: 1.81×10⁻⁴ °C⁻¹.