A-level Physics (Advancing Physics)/Heat and Energy/Worked Solutions

1. Carbon dioxide sublimes at 195°K. Roughly what energy per. particle does this correspond to?

$E \approx kT = 1.38 \times 10^{-23} \times 195 \approx 10^{-21}\mbox{ J particle}^{-1}$

2. A certain chemical reaction requires particles with mass of the order 10-26 to move, on average, at 10ms-1. Roughly what temperature does this correspond to?

$E_k = \frac{1}{2}mv^2 = 0.5 \times 10^{-26} \times 10^2 = 5 \times 10^{-25}$

$5 \times 10^{-25} = kT$

$T = \frac{5 \times 10^{-25}}{1.38 \times 10^{-23}} \approx 10^{-2}$ °K

3. The boiling point of water is 100°C. Roughly what energy per. particle does this correspond to?

100°C = 373°K

$E \approx kT = 1.38 \times 10^{-23} \times 373 \approx 5 \times 10^{-21}\mbox{ J particle}^{-1}$

4. Thermionic emission from copper requires around 5eV of energy per. particle. How hot will the wire be at this energy level?

5eV = 5 x 1.6 x 10-19 = 8 x 10-19 J particle-1

$T = \frac{8 \times 10^{-19}}{1.38 \times 10^{-23}} \approx 6 \times 10^4$ °K