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- TL;DR Summary
- How does putting a cover affect the pressure inside a glass filled with air?

Let's consider an uncovered glass. Air particles are present in the glass.

$$ P_1 = P_a$$ $$P_2 =P_1 +\rho gh = P_a +\rho g h$$where ##P_A## is atmospheric pressuere and ##\rho ## is air density.

Now, if I cover the glass with a plastic card, then what is ## P_1##?

$$P_2 =P_1 +\rho gh $$

1) ## P_1 ## is pressure due to motion of air particles and the air particles near the cover interact with the cover and its speed may change and hence ##P_1## may be less or more than ##P_a##.

2) Following three forces are acting on the cover:

a) force due to pressure ##P_1## of air particles

b) normal force N due to glass walls

c) cover's weight W

Applying Newton's first law gives,

$$ P_1 A+ N = W$$ $$P_1 A = W - N$$

Now, since normal force is self-adjustable, let's take a light plastic card such that N = 0. Hence, in this case ##P_1 A = W ##.

For a plastic card with mass 20g and area 20cm

So, the conclusion is: putting a cover reduces the pressure of air inside the glass. Is this correct?

$$ P_1 = P_a$$ $$P_2 =P_1 +\rho gh = P_a +\rho g h$$where ##P_A## is atmospheric pressuere and ##\rho ## is air density.

Now, if I cover the glass with a plastic card, then what is ## P_1##?

$$P_2 =P_1 +\rho gh $$

1) ## P_1 ## is pressure due to motion of air particles and the air particles near the cover interact with the cover and its speed may change and hence ##P_1## may be less or more than ##P_a##.

2) Following three forces are acting on the cover:

a) force due to pressure ##P_1## of air particles

b) normal force N due to glass walls

c) cover's weight W

Applying Newton's first law gives,

$$ P_1 A+ N = W$$ $$P_1 A = W - N$$

Now, since normal force is self-adjustable, let's take a light plastic card such that N = 0. Hence, in this case ##P_1 A = W ##.

For a plastic card with mass 20g and area 20cm

^{2}, ## P_1 = 10 Pa## which is lower than the atmospheric pressure.So, the conclusion is: putting a cover reduces the pressure of air inside the glass. Is this correct?