Finding change in height of fluid in U tube from change in T

[JoeyBob]

Homework Statement

See attached

Relevant Equations

change P = (change h)*g*density

So first I converted the density from g/cm^3 to kg/cm^3 (it wants the answer in cm). This gives me a density of 0.01356 kg/cm^3.

Then I thought about the relationship of pressure and temperature. Since volume remains constant and temperature is the only variable changing, the change in pressure should be proportional to the change in temperature. A change in 56.3 degrees therefore should be a change in 56.3 pascals.

Now when I plug the numbers in, change in h=56.3/(9.8*0.01356) I get the incorrect answer of 423.67 cm. The correct answer is 21.31, which is not just off from unit conversions.

 

[haruspex]

the change in pressure should be proportional to the change in temperature. A change in 56.3 degrees therefore should be a change in 56.3 pascals.

Proportional doesn't mean numerically equal to, especially when they are of different dimension. If you were working in Fahrenheit would a change of 56.3 degrees also mean a change of 56.3Pa?
The absolute temperature is proportional to the pressure: P/T is constant.

 

[JoeyBob]

Proportional doesn't mean numerically equal to, especially when they are of different dimension. If you were working in Fahrenheit would a change of 56.3 degrees also mean a change of 56.3Pa?
The absolute temperature is proportional to the pressure: P/T is constant.

That makes sense. But then how would I calculate change in pressure if all I know from PV=nRT is initial temperature and final temperature?

 

[haruspex]

That makes sense. But then how would I calculate change in pressure if all I know from PV=nRT is initial temperature and final temperature?

... and initial pressure.

 

[JoeyBob]

... and initial pressure.

Where? Even if I had pressure, I still wouldn't have the moles nor volume. I just know what's constant.

 

[haruspex]

Where?

what is h initially?

 

[JoeyBob]

what is h initially?

0. But it doesn't make sense that pressure would be 0 to me. True vacuums don't exist.

 

[haruspex]

0. But it doesn't make sense that pressure would be 0 to me. True vacuums don't exist.

It doesn’t mean the pressure is zero.. unless the entire apparatus is in outer space.

 

[JoeyBob]

It doesn’t mean the pressure is zero.. unless the entire apparatus is in outer space.

Do I use the equation P(h)=P_0+density*g*h?

 

[haruspex]

Do I use the equation P(h)=P_0+density*g*h?

Say what you think. Does it apply here? If so, what are P(0), P(h) etc. in this context?

 

[Chestermiller]

If h is zero to start with, and the outside pressure is 1 atm, what is the starting pressure inside the gas reservoir?