A uniform glass tube, closed at one end, contains a column of mercury 5 cm long. The length of the trapped air column is 26 cm when the tube is held vertically upright. When the tube is inverted, the

In Figure (a) (tube upright):
Length of air column, $L_1 = 26 \text{ cm}$
Length of mercury thread, $h = 5 \text{ cm}$
The pressure of the trapped air is the atmospheric pressure plus the pressure due to the mercury column:
$P_1 = P_{atm} + h = P_{atm} + 5 \text{ cmHg}$

In Figure (b) (tube inverted):
Length of air column, $L_2 = 30 \text{ cm}$
Length of mercury thread, $h = 5 \text{ cm}$
The pressure of the trapped air is the atmospheric pressure minus the pressure due to the mercury column:
$P_2 = P_{atm} - h = P_{atm} - 5 \text{ cmHg}$

Assuming the temperature remains constant, Boyle's Law states $P_1V_1 = P_2V_2$.
Since the tube has a uniform cross-sectional area $A$, the volume of the air column is $V = LA$.
So, $P_1L_1A = P_2L_2A$, which simplifies to $P_1L_1 = P_2L_2$.

The value of the atmospheric pressure is $\boxed{\text{70 cmHg}}$.

c) A steel cylinder of capacity $0.5 \text{ m}^3$ contains nitrogen at a pressure of $30,000 \text{ Pa}$ when the temperature is $27^\circ \text{C}$. What will be the pressure of nitrogen if it is allowed to flow into another cylinder of capacity $9.5 \text{ m}^3$ with the temperature reduced to $-23^\circ \text{C}$?

Initial volume, $V_1 = 0.5 \text{ m}^3$
Initial pressure, $P_1 = 30,000 \text{ Pa}$
Initial temperature, $T_1 = 27^\circ \text{C}$. Convert to Kelvin:
$T_1 = 27 + 273.15 = 300.15 \text{ K}$

The gas flows into another cylinder of capacity $9.5 \text{ m}^3$. The total final volume is the sum of the capacities of both cylinders:
Final volume, $V_2 = 0.5 \text{ m}^3 + 9.5 \text{ m}^3 = 10 \text{ m}^3$
Final temperature, $T_2 = -23^\circ \text{C}$. Convert to Kelvin:
$T_2 = -23 + 273.15 = 250.15 \text{ K}$
Final pressure, $P_2 = ?$

The Combined Gas Law is given by:

The pressure of nitrogen will be $\boxed{\text{1250.12 Pa}}$.

16. a) State Archimedes principle. Archimedes' principle states that when an object is wholly or partially immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the object.

b) State one way of making a hydrometer more sensitive.
One way to make a hydrometer more sensitive is to increase the length of its stem or decrease the diameter of its stem.