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A simple barometer tube contains some air in it. The length of

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A simple barometer tube contains some air in it. The length of the tube above the mercury level in the trough is 80 cm. The height of mercury in the tube is 71 cm at normal atmospheric pressure. What is the actual decrease in the atmospheric pressure if the barometer reads 65 cm?

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A simple barometer tube contains some air in it. The length of the tube above the mercury level in the trough is 80 cm. The height of mercury in the tube is 71 cm at normal atmospheric pressure. What is the actual decrease in the atmospheric pressure if the barometer reads 65 cm?

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Text solutionVerified

P^{'} =

pressure due to entrapped air

+

pressure due to the mercury column
Let pressure due to entrapped air be

P_{2}

and volume of air column be

V_{2}

Here, we have pressure due to the mercury column

= 65 cm

The total height of barometer

= 80 + 71 = 151 cm

Thus, the length of the air column in this case

= 151 - 65 = 86 cm

So,

V_{2} = 86 a

P^{'} = P_{2} + 65 cm

Also according to Boyle's Law, we have

P_{1} V_{1} = P_{2} V_{2}

P_{2} = \frac{P _{1} V _{1}}{V _{2}}

Substituting this value, we get

P^{'} = \frac{P _{1} V _{1}}{V _{2}} + 65 cm

P^{'} = \frac{P _{1} ( 80 a )}{86 a} + 65 cm

P^{'} = \frac{40 P _{1}}{43} + 65

P = P_{1} + 71 cm

and

P^{'} = \frac{40 P _{1}}{43} + 65 cm

P - P^{'} = P_{1} + 71 - (\frac{40 P _{1}}{43} + 65)

P - P^{'} = P_{1} (\frac{3}{43}) + 6

At normal conditions, we have

P_{1} = 1 atm

P - P^{'} = 1 (\frac{3}{43}) + 6

P - P^{'} = 6.069 atm

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Question Text	A simple barometer tube contains some air in it. The length of the tube above the mercury level in the trough is 80 cm. The height of mercury in the tube is 71 cm at normal atmospheric pressure. What is the actual decrease in the atmospheric pressure if the barometer reads 65 cm?
Topic	Gravitation
Subject	Science
Class	Class 9
Answer Type	Text solution:1
Upvotes	143

A simple barometer tube contains some air in it. The length of the tube above the mercury level in the trough is 80 cm. The height of mercury in the tube is 71 cm at normal atmospheric pressure. What is the actual decrease in the atmospheric pressure if the barometer reads 65 cm?

Text solutionVerified

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A simple barometer tube contains some air in it. The length of the tube above the mercury level in the trough is 80 cm. The height of mercury in the tube is 71 cm at normal atmospheric pressure. What is the actual decrease in the atmospheric pressure if the barometer reads 65 cm?

Text solutionVerified

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