Gas Law - Numerical Problems

Example 1:
A fish releases a bubble of air of volume 1cm³ at the bottom of a lake. The depth of the lake is 10m. Find the volume of the bubble when it reaches the surface of the pond. (Assume that the atmospheric pressure is equal to 10m of water)

Answer:
V₁ = 1cm³
P1 = 20m water
V₂ = ?
P2 = 10m water
$$\begin{array}{l}{P}_1{V}_1=P_2{V}_2\\ (20)(1)=(10)V_2\\ V_2=\frac{20}{10}=2c{m}^3\end{array}$$

Example 2:
An iron cylinder containing gas with pressure 200kPa when it is kept is a room of temperature 27°C. What is the pressure of the gas when the cylinder is located outdoor where the temperature is 35°C.

Answer:
P₁ = 200kPa
T₁ = 273 + 27 = 300K
P₂ = ?
T₂ = 273 + 35 = 308K
$$\begin{array}{l}\frac{P_1}{T_1}=\frac{P_2}{T_2}\\ \frac{(200000)}{(300)}=\frac{P_2}{(308)}\\ P_2=\frac{(308)(200000)}{(300)}=205kPa\end{array}$$

Example 3:

The figure shows some air trapped in a capillary tube. Given that the temperature of the air is 27°C. Find the length of the air column when the temperature of the air is increased to 87°C.

Answer:
V₁ = 6cm
T₁ = 273 + 27 = 300K
V₂ = ?
T₂ = 273 + 87 = 360K
$$\begin{array}{l}\frac{V_1}{T_1}=\frac{V_2}{T_2}\\ \frac{(6)}{(300)}=\frac{V_2}{(360)}\\ V_2=\frac{(360)(6)}{(300)}=7.2cm\end{array}$$