Temperature & Kinetic Energy

Particles in gases usually have a range of speeds
The average random kinetic energy of the particles E_k can be calculated using the equation

$E_{k} = \frac{3}{2} k_{B} T$

Where:
- E_k = average random kinetic energy of the particles in joules (J)
- k_B = 1.38 × 10^–23 J K^–1(Boltzmann's constant)
- T = absolute temperature in kelvin (K)

This tells us that the absolute temperature of a body is directly proportional to the average kinetic energy of the molecules within the body

Graph of Absolute Temperature against Kinetic Energy of Molecules, for IB Physics Revision Notes

The surface temperature of the Sun is 5800 K and contains mainly hydrogen atoms.

Calculate the average speed of the hydrogen atoms, in km s⁻¹, near the surface of the Sun.

Answer:

Step 1: List the known quantities

Step 2: Equate the equations relating kinetic energy with temperature and speed

$\frac{3}{2} k_{B} T = \frac{1}{2} m_{p} v^{2}$

Step 3: Rearrange for average speed and calculate

$\frac{3 k_{B} T}{m_{p}} = v^{2}$

$v = \sqrt{\frac{3 k_{B} T}{m_{p}}} = \sqrt{\frac{3 \times (1.38 \times 10^{- 23}) \times 5800}{1.673 \times 10^{- 27}}}$

Average speed: v = 11 980 m s⁻¹ = 12 km s⁻¹

Temperature & Kinetic Energy (SL IB Physics)