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