IB Physics SL B.1.5 Kelvin Temperature and Kinetic Energy

Practise relating absolute temperature to mean translational kinetic energy and using particle mass to compare molecular speeds for gases at the same or different temperatures.

Exam points

convert Celsius to kelvin before using mean translational energy 3kBT/2
state that ideal-gas particles at the same temperature have equal mean kinetic energy
derive rms speed from 3kBT/2 = mv²/2 and account for molecular mass in kilograms

[Maximum number: 2]

A mass of 1.0 kg of water is brought to its boiling point of $100^{\circ} \mathrm{C}$ using an electric heater of power 1.6 kW .

The molar mass of water is $18 \mathrm{~g} \mathrm{~mol}^{-1}$ . Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.

$E_k=\frac32(1.38\times10^{-23})(373)=7.7\times10^{-21}\ \mathrm{J}$ .
$v=\sqrt{\frac{3\times1.38\times10^{-23}\times6.02\times10^{23}\times373}{0.018}}=720\ \mathrm{m\ s^{-1}}$ .

v=\sqrt{\frac{3(1.38\times10^{-23})(6.02\times10^{23})(373)}{0.018}}=720\ \mathrm{m\ s^{-1}}

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B.1.5—Kelvin temperature and kinetic energy question 1