# Length of the Air column

shaiqbashir
A vertica cylindrical Tank of length greater rgab 76cm has its top end closed by a tightly fitting frictionless piston of negligible weight. The air inside the cylinder is at an absolute pressure of 1 atm. The piston depressed by pouring mercury on it slowly, so that the temperature of air is maintained constant. What is the length of the air column where the mercury starts to spill over?

## Answers and Replies

faust9
This has the distinct taste of a homework question and as such should probably have been posted there. Additionally, you'll get a lot more help if you actually ask a question about the problem rather than simply posting the problem. I know I can solve this type of problem; however, simply posting the solution would do you very little good.

So, on that note, how much Hg will there be before it spills over? Hint, you are balancing forces here. The force of Mercury pushing down on the piston vs the force of the compressed gas pushing up on the piston. Think about this force relationship and how it relates to these two fluids. How much downward force is produced by a 74cm column of Hg and how much upward force is produced by compressing 1amt of air from 76cm to 2cm? I think once you balance the forces you'll find your answer.

Good luck.

shaiqbashir
thanks for ur precious help!

but would u like to tell me that what is the reason for taking 74 cm when it is not given in the question.
Further more! i want u to tell me the right answer only my dear.

im not a cheater, i want to confirm my answer only

Staff Emeritus
Gold Member
shaiqbashir said:
im not a cheater, i want to confirm my answer only
In that case post your answer as well as how you arrived at it. Once you do that, someone may respond...not before.

<moving thread to HH>

faust9
shaiqbashir said:
thanks for ur precious help!

but would u like to tell me that what is the reason for taking 74 cm when it is not given in the question.
Further more! i want u to tell me the right answer only my dear.

im not a cheater, i want to confirm my answer only

As Gokul said I'm not going to tell you the answer. I, or many others, can verify your answer though. I chose 74(because the length of the column was 76) to get you thinking along the lines of the Weight of the column of Hg vs the force of the compressed gas pushing back against the Hg.

shaiqbashir
Hi Guys!

Well thanks a lot for ur help, this problem has now really become an important one for me. Just can't get the correct way to go, now can u remind me how to write the force of a compressing gas with which it is balancing the upward force. Secondly, how it is possible to determine the length of the column when we don't know the area at all?

i have been given the pressure which is 1 atm. now i really cannot understand your logic of 74 cm. Please! i request you to tell me this in detail. furthermore i want to remind you here that in the question it is given that the length of the air column is GREATER than 76 cm so i can't understand ur logic of making 74 cm. Please if u don't want to tell me the correct answer don't tell me then but atleast make the question clarified to me.

Thanks a lot and Good Bye

Homework Helper
So when you told us before that you had already solved the problem and only wanted someone to give you the correct answer to verify your answer, exactly what did you mean?

(No one ever said that 74 cm was the correct answer. He was just suggesting that try calculating the forces using that value in order to see what kind of equation you had to set up!)

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Staff Emeritus