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Explain why the height of mercury in a barometer is independent of the cross-sectional area of the tube. Would the barometer still work if the tubing were tilted at an angle, say $15^{\circ}$ (see Figure 5.3 )?

The force required to raise the mercury level to a height of $h$ is equal to the weight of the mercury.\[F=m g=\rho g h A\]We can therefore express the heighth in terms of $F$ as\[h=\frac{F}{\rho g A}\]Pressure is defined as force per unit area. Thus, the amount of pressure required to give a force of $F$ is\[P=\frac{F}{A} \Rightarrow F=P \cdot A\]Therefore, the amount of pressure required to raise the level to a height of $h$ is\[h=\frac{F}{\rho g A}=\frac{P \cdot A}{\rho g A}=\frac{P}{\rho g}\]since $A$ is cancelled out, the height of the mercury level is independent of the cross-sectional area. If the tubing were tilted at an angle of $15^{\circ},$ the vertical height of the liquid would be the same so it would still work.

Chemistry 101

Chapter 5

Gases

University of Central Florida

Rice University

University of Maryland - University College

Lectures

05:03

In physics, a gas is one of the three major states of matter (the others being liquid and solid). A gas is a fluid that does not support tensile stress, meaning that it is compressible. The word gas is a neologism first used by the early 17th-century Flemish chemist J.B. van Helmont, based on the Greek word ("chaos"), the simplest of all the elemental forms of matter.

04:46

In physics, thermodynamics is the science of energy and its transformations. The three laws of thermodynamics state that energy can be exchanged between physical systems as heat and work; that the total energy of a system can be calculated by adding up all forms of energy in the system; that energy spontaneously flows from being localized to becoming dispersed, spread out, or uniform; and that the entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

04:45

Explain why the height of …

01:15

03:27

00:42

Why does the size of the c…

00:18

Why doesn’t the size of th…

01:18

A barometer is constructed…

01:19

Suppose the mercury used t…

01:08

If you use water instead o…

01:46

Pressure is defined as for…

01:23

Suppose you make a mercury…

So for this question, you have to understand that the force required to raise the mercury level to height off H is equal to the weight off the mercury. Which means that the force as equals, two mg mass times gravity equals two PG, great times, height and area. Then, from this equation, we can express that the heights as equals to the force divided by P G eight. Right. So we just put the H to the left side forest to the wreck size as a little bit algebra. So we get this equation and then you know that pressure is also equals to force divided by area, which means that force can be right into pressure times area. From this, we substitute back into the equation. So which means that height is also pressure Times area divided by P. G. A. Okay, you can see a from the top and a from the bottom can actually canceled out when they can canceled out. It means that the heights does not depend on the area off the cross section and only depends on the pressure and the P and G. So it means that H is independent to the area

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