Physics: Measuring Temperature with Mercury Question

[justadream]

"With only hte vacuum and mercury plug above, the gas is at constant pressure equal to density *g*h.". Density is the density of the mercury.

Can someone explain this? I thought the force being exerted was the weight of the mercury which should be mgh = density * volume * g* h

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[MedHopeful20134]

Weight of the mercury is m * g = Density * Volume * g (not "mgh = density * volume * g* h")
Notice, when you multiply density with volume, you get units of mass (which makes sense). Mass times gravity is weight or force due to gravity.

Pressure is force over an area, which is what the solution indicates, density * g * h.
Pressure over the gas is pressure due to the mercury plug.
You are correct when you say force is exerted by the mercury on top of the gas, however, you will have to divide it by area to get pressure or you can just use the formula (density * g * h), where h is height of the mercury plug.

 

[justadream]

@MedHopeful20134

Good catch on the weight!

So where does the volume term go in the answer?

Should it be:
(density * volume * g) / area ?

 

[MedHopeful20134]

@justadream Yup, you are right.


Pressure = Force / Area = (density * volume * g)/(pi * r ^2)
This is same as = (density * pi * r ^ 2 * h * g)/(pi * r ^2) (underlined term represents volume of a cylinder, as in a thermometer tube)
Now, (pi * r ^2) term cancels out giving you:

Pressure = density * h * g (which is what the solution states and easier to apply).

 

[Cawolf]

That's a good formula to know for pressure heads and the like.