Edexcel A-Level Physics Ideal Gas Equation

Practise Edexcel A-Level Physics ideal gas equation questions by using pV=NkT with Kelvin temperature, volumes, molecule counts and pressure.

Exam points

calculate molecule number, pressure or volume using pV = NkT and Kelvin temperature
combine pV = NkT with spherical volume, mass per molecule or pressure-difference data
interpret ideal-gas conditions such as constant temperature, volume or molecule number

[Maximum number: 6]

According to the Football Association (FA) rules, the football used in a professional match should have a circumference of between 68.0 cm and 70.0 cm . The pressure of the air in the football must be between 60 kPa and 110 kPa above atmospheric pressure.

A football was inflated with air at a temperature of $16.0^{\circ} \mathrm{C}$ . When inflated, the circumference of the football was 68.5 cm and it contained $2.50 \times 10^{23}$ molecules of air.

Deduce whether this football met the FA rules.
atmospheric pressure =105 kPa

Use $C=2\pi r$ , $V=4\pi r^3/3$ , convert $16.0^\circ\mathrm{C}$ to 289 K, and use pV=NkT. This gives absolute pressure $1.84\times10^5\,\mathrm{Pa}$ and excess pressure $7.9\times10^4\,\mathrm{Pa}=79\,\mathrm{kPa}$ . The circumference is $68.5\,\mathrm{cm}$ and the excess pressure is within 60–110 kPa, so the ball meets the rules.

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5.3.130 - Ideal gas equation question 1