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**1. Homework Statement**

vertical glass tube with height of 2H. H is 760mm.

the lower half is full of an unknown gas. the upper half is full of mercury.

The gas gets heated so it pushes the mercury out of the glass tube.

What temperature must the gas be heated to?

here is the photo if, for some reason, it doesn't show up http://i.imgur.com/p1H9YyR.jpg

**2. Homework Equations**

## p_1 = -p_0 - \rho h g ##

## p_2 = -p_0 ## because tube doesn't have mercury

## h = H = 760 mm ##

## \rho h g = 10^5 Pa##

**3. The Attempt at a Solution**

## \frac{p*V}{T} = ct ##

## \frac{p_1*V_1}{T_1}=\frac{p_2*V_2}{T_2} ##

## \frac{p_1*V_1}{p_2*V_2}=\frac{T_1}{T_2} ##

## \frac{(-p_0 - \rho h g) S H}{(-p_0) S 2 H} = \frac{T_1}{T_2} ##

## \frac{-p_0 - \rho h g}{-2p_0} = \frac{T_1}{T_2} ##

## \frac{p_0+ \rho h g}{2p_0} = \frac{T_1}{T_2} ##

but ## \rho h g = p_0 ##

so ##\frac{T_1}{T_2} = 1 ##

and ## T_1 = T_2 ##