The fuel used in a camping stove is butane, which is stored in a canister as shown - Edexcel - A-Level Physics - Question 14 - 2023 - Paper 2

To find the number of molecules, we can use the Ideal Gas Law, which states:

$PV = nRT$

Where:

• P = pressure = 220 kPa = 220,000 Pa
• V = volume of the gas
• n = number of moles
• R = ideal gas constant = 8.314 J/(mol·K)
• T = temperature in Kelvin = 21 °C + 273 = 294 K

1. Calculate the volume of the cylinder:

   • Radius (r) = 0.11 m
   • Length (L) = 0.23 m
   • Volume (V) = πr²L = π(0.11)^2(0.23)
   • V ≈ 0.0084 m³

2. Calculate the number of moles (n):

   • Rearranging the Ideal Gas Law: $n = \frac{PV}{RT}$
   • Substitute:
   n ≈ 9.04 ext{ moles}$$

3. Calculate the number of molecules:

   • Number of molecules = n × Avogadro's number (6.022 × 10^23)
   • Number of molecules ≈ 9.04 × 6.022 × 10^23 ≈ 5.44 × 10^{24} ext{ molecules}

The r.m.s. speed (v_rms) of gas molecules can be calculated using the formula:

$v_{rms} = \sqrt{\frac{3kT}{m}}$

Where:

• $k$ is the Boltzmann constant ≈ $1.38 × 10^{−23} ext{ J/K}$
• $T$ is the temperature in Kelvin = 294 K
• $m$ is the mass of a butane molecule = $9.6 × 10^{-26} ext{ kg}$

Substituting the values:

1. Calculate the r.m.s. speed: $v_{rms} = \sqrt{\frac{3(1.38 × 10^{−23})(294)}{9.6 × 10^{−26}}}$
   • Perform the calculations:
   • $v_{rms} ≈ 360 ext{ m/s}$