Define pressure - Leaving Cert Physics - Question b - 2007

To demonstrate that the atmosphere exerts pressure, the following experiment can be conducted:

Apparatus:

• A glass of water
• A piece of cardboard

Procedure:

1. Fill the glass about three-quarters full with water.
2. Place the cardboard over the top of the glass.
3. Holding the cardboard in place, quickly invert the glass so that the cardboard is on top.
4. Remove your hand from the cardboard.
5. Observe that the cardboard remains in place and the water does not spill out.

Observation: This experiment shows that the atmospheric pressure acting on the cardboard is greater than the weight of the water pulling down, thus demonstrating that the atmosphere exerts pressure.

Boyle’s Law states that for a fixed mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, this can be expressed as:

$P V = \text{constant}$

where $P$ is the pressure and $V$ is the volume.

Using Boyle’s Law, we can set up the equation based on the initial and final conditions:

1. At ground level:

   • Initial Volume, $V_1 = 2 \, \text{m}³$
   • Initial Pressure, $P_1 = 1000 \, \text{hPa}$

2. At height, where:

   • Final Pressure, $P_2 = 500 \, \text{hPa}$
   • Final Volume, $V_2 = ?$

According to Boyle's Law:

$P_1 V_1 = P_2 V_2$

Substituting the known values, we have:

$1000 \, \text{hPa} \times 2 \, \text{m}³ = 500 \, \text{hPa} \times V_2$

Simplifying gives us:

$V_2 = \frac{1000 \times 2}{500} = 4 \, \text{m}³$

As the balloon continues to rise, the atmospheric pressure around it will decrease. Since the temperature remains constant, according to Boyle’s Law, the volume of the balloon will increase. Eventually, if the volume becomes too large, the balloon may burst due to the differences in pressure between the inside and outside.