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