Pressure in Manometer

[AwayFromReality]

TBR Example 6.15
What is the pressure in atmospheres of a column of gas in a closed tube above mercury if the height difference at sea level between a connected column of mercury open to the atmosphere and the closed column above mercury is 317 mm?

The answer is 0.583atm

In the explanation they mention that since the Height difference (delta H) is 317, the pressure difference (delta p) is also 317. From there they said the answer could be either 760torr-317torr =443torr or 760+317torr=1077torr but the answer choices only have 443torr so that is what is chosen as correct.

I don't understand how Height Difference EQUALS Pressure Difference. I thought the equation for Pressure difference was: Delta P = (Density)(g)(Height Difference). So How can we take 317 for Pressure difference directly?

EDIT: I think I figured it out. Since this manometer uses Mercury, one mm of height difference is equal to 1 torr. Therefore we can easily convert between Height and Pressure difference. Is this theory correct?

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[santeprof]

The classical definition of Torr is 1 mm of Hg. Look at wikipedia. Does this help?

 

[kraskadva]

Height difference = pressure difference for torr/mmHg, since that's how the unit is defined. For other pressure units you would have to convert.

 

[AwayFromReality]

The classical definition of Torr is 1 mm of Hg. Look at wikipedia. Does this help?

Yup that helps

Height difference = pressure difference for torr/mmHg, since that's how the unit is defined. For other pressure units you would have to convert.

Yeah that makes sense now. So for all other pressure units we use the Delta P equation which includes knowing the density of the gas at the closed end?

 

[kraskadva]

Yup that helps
Yeah that makes sense now. So for all other pressure units we use the Delta P equation which includes knowing the density of the gas at the closed end?

Yes to the equation, but it's a vacuum at the closed end, not a gas. You would need the density of the liquid in the column, since that's what has to be lifted by the external pressure.

 

[AwayFromReality]

Yes to the equation, but it's a vacuum at the closed end, not a gas. You would need the density of the liquid in the column, since that's what has to be lifted by the external pressure.

Great thanks again for your help