State Boyle's law - Leaving Cert Physics - Question (a) - 2011

1. Apparatus: Use a container filled with water, such as a glass or a beaker, and a piece of cardboard or a lid.

2. Procedure:

   • Fill the glass with water, ensuring it is full.
   • Cover the top of the glass with the cardboard or lid, ensuring it forms a tight seal.
   • Carefully invert the glass while holding the cardboard in place.

3. Observation/Conclusion: When you release the cardboard, the water stays in the glass due to atmospheric pressure holding the cardboard against the top of the water. This experiment demonstrates that the atmosphere exerts a pressure that counteracts the force of gravity acting on the water.

Using Boyle's law, we can determine the available volume of gas at the top of Mount Everest. The formula is:

$P_1 V_1 = P_2 V_2$

where:

• $P_1 = 4.2 \times 10^6 \text{ Pa}$ (initial pressure),
• $V_1 = 5.0 \text{ litres}$ (initial volume),
• $P_2 = 3.0 \times 10^4 \text{ Pa}$ (pressure at the top of Mount Everest).

Rearranging the formula to solve for $V_2$ gives us:

$V_2 = \frac{P_1 V_1}{P_2}$

Substituting the values:

$V_2 = \frac{(4.2 \times 10^6)(5.0)}{3.0 \times 10^4} \text{ litres} = \frac{2.1 \times 10^7}{3.0 \times 10^4} \approx 700 \text{ litres}$

Thus, approximately 700 litres of gas will be available at the top of Mount Everest when the gas is released from the tank.