A thin tube closed at the top and open to the atmosphere at the bottom contains a 12 cm high column of air trapped above a 20 cm column of mercury. If the tube is flipped so that the closed end is now at the bottom, what is the new height of the trapped column of air

The column height of air after the inversion is 7 cm.

Step-by-step explanation:

The initial pressure balance is given as

P_1+20 cm=76 cm of Hg

P_1=76-20 cm of Hg

P_1=56 cm of Hg

The initial volume of the air with cross sectional area as 12 cm2 and the length of air column as 12 is given as V_1=12 cm *1 =12 cm3

After the inversion

P_2=20 cm+76 cm of Hg

P_2=96 cm of Hg

The volume of the air after the inversion with cross sectional area as 1 cm2 and the length of air column as x is given as V_2=x *1 =x cm3

Now as temperature is constant and the cross sectional area is also constant so

So the column height of air after the inversion is 7 cm.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

step-by-step explanation: