Explain why electricity transmission cables are left sagging and calculate the height of a mountain given the pressure difference in cm of Hg.

Electricity transmission cables are left sagging between pylons to allow for thermal expansion and contraction. This prevents the cables from becoming too taut and snapping during cold weather when they contract, or sagging excessively and touching the ground during hot weather when they expand.

The pressure difference between the base and the top of the mountain can be expressed in terms of the mercury column and the air column.
Given:
Pressure at base, $P_1 = 75.0 \text{ cm of Hg}$
Pressure at top, $P_2 = 60.0 \text{ cm of Hg}$
Density of air, $\rho_{air} = 1.25 \text{ kg/m}^3$
Density of mercury, $\rho_{Hg} = 13600 \text{ kg/m}^3$
Acceleration due to gravity, $g \approx 9.81 \text{ m/s}^2$ (or $10 \text{ m/s}^2$ if not specified, but it will cancel out here).

The pressure difference in terms of mercury column is:

Convert this height to meters:

The pressure difference can also be expressed as $\Delta P = \rho g h$.
So, the pressure difference due to the mercury column is:

The pressure difference due to the height of the mountain (air column) is:

Equating the two expressions for $\Delta P$:

We can cancel $g$ from both sides:

Now, solve for $h_{mountain}$:

Substitute the given values:

The height of the mountain is $\boxed{\text{1632 m}}$.

Two factors that would raise the boiling point of water are:

• Increasing the external pressure on the water.
• Adding impurities (solutes) to the water.

Given:
Initial volume of water in burette = $2.5 \text{ cm}^3$
Number of drops added = 40
Volume per drop = $0.05 \text{ cm}^3$

First, calculate the total volume of the added drops:

Now, calculate the new reading in the burette by adding the initial volume and the total volume of drops:

The new reading would be $\boxed{\text{4.5 cm}^3}$.