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?

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

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?

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

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

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

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

100 °C = 373°K

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

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