A glass tube has one end in a dish of mercury and the other...

A glass tube has one end in a dish of mercury and the other end closed by a stopcock. The distance from the surface of the mercury to the bottom of the stopcock is 850 $\mathrm{mm}$ . The apparatus is at $25^{\circ} \mathrm{C},$ and the mercury level in the tube is the same as that in the dish. (a) Show on drawing $(1)$ what the approximate level of mercury in the tube will be when the temperature of the entire apparatus is lowered from $$+25^{\circ} \mathrm{C}$ to $-25^{\circ} \mathrm{C} .$$ (b) Show on drawing $(2)$ what the approximate level of mercury in the tube will be when a vacuum pump is connected to the top of the tube, the stopcock is opened, the tube is evacuated, the stopcock is closed, and the pump is removed. (c) Show on drawing (3) what the approximate level of mercury in the tube will be when the stopcock in drawing (2) is opened.

A glass tube has one end in a dish of mercury and the other end closed by a stopcock. The distance from the surface of the mercury to the bottom of the stopcock is 850 $\mathrm{mm}$ . The apparatus is at $25^{\circ} \mathrm{C},$ and the mercury level in the tube is the same as that in the dish.
(a) Show on drawing $(1)$ what the approximate level of mercury in the tube will be when the temperature of the entire apparatus is lowered from $$+25^{\circ} \mathrm{C}$ to $-25^{\circ} \mathrm{C} .$$
(b) Show on drawing $(2)$ what the approximate level of mercury in the tube will be when a vacuum pump is connected to the top of the tube, the stopcock is opened, the tube is evacuated, the stopcock is closed, and the pump is removed.
(c) Show on drawing (3) what the approximate level of mercury in the tube will be when the stopcock in drawing (2) is opened.

Key Concepts

Vacuum Effects

The creation of a vacuum in a portion of the apparatus changes the pressure conditions acting on the liquid. By evacuating the air from a tube, the pressure above the liquid is greatly reduced, resulting in alterations to the equilibrium level of the liquid based on the imbalance between the vacuum pressure above and the atmospheric pressure acting at the reservoir. This concept is important for analyzing systems where air is removed and for understanding the subsequent behavior of the liquid column.

Barometric Principle

The barometric principle involves the concept of using a column of liquid, such as mercury, to measure atmospheric pressure. In a mercury barometer, the weight of the mercury column in a tube is balanced by the atmospheric pressure acting on the mercury reservoir. This principle is foundational in understanding how pressure differences can cause changes in the liquid level when one end of a tube is exposed to atmospheric pressure and the other is altered by vacuum or sealed conditions.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. This pressure is determined by the density of the fluid, gravitational acceleration, and the height of the fluid column. Understanding hydrostatic pressure is essential to determine the balance of forces acting on a fluid in a container and to predict the liquid level changes under different conditions.

Thermal Expansion

Thermal expansion refers to the tendency of matter to change in volume in response to a change in temperature. In liquids, including mercury, an increase in temperature typically leads to expansion (increase in volume) and a decrease in density, whereas a decrease in temperature results in contraction (decrease in volume) and an increase in density. This concept is crucial in predicting how the level of a liquid in a container will change when the temperature varies.

Transcript

Please give Ace some feedback