Question 2.
A vertical glass tube of cross section S = 1.0 cm2 contains unknown amount of
hydrogen. The upper end of the tube is closed. The other end is opened and is immersed in a
pan filled with mercury. The tube and the pan are placed in a sealed chamber containing air at
temperature T = 273 K and pressure P = 1.334105 Pa. Under these conditions the height of
0 0
mercury column in the tube above the mercury level in the pan is h = 0.70 m.
0
One of the walls of the chamber is a piston, which expands the air isothermally to a
pressure of P = 8.00104 Pa. As a result the height of the mercury column in the tube
1
decreases to h = 0.40 m. Then the chamber is heated up at a constant volume to some
1
temperature T until the mercury column rises to h = 0.50 m. Finally, the air in the chamber
2 2
is expanded at constant pressure and the mercury level in the tube settles at h = 0.45 m above
3
the mercury level in the pan.
Provided that the system is in mechanical and thermal equilibrium during all the
processes calculate the mass m of the hydrogen, the intermediate temperature T , and the
2
pressure P in the final state.
The density of mercury at temperature T is = 1.36104 kg/m3, the coefficient of
0 0
expansion for mercury = 1.8410–4 K–1, and the gas constant R = 8.314 J/(molK). The
thermal expansion of the glass tube and the variations of the mercury level in the pan are not
considered.
Hint. If T is the interval of temperature variations of the system then T = x << 1 In
1
that case you can use the approximation: 1 x.
1 x