David Sang and Graham Jones Solutions for Chapter: Ideal Gases, Exercise 7: Questions

The Boltzmann constant $\mathrm{k}$ is equal to $\frac{R}{N_A}$. For standard values of $\mathrm{R}$ and $N_{\mathrm{A}}$, show that $\mathrm{k}$ has the value $1.38\times {10}^{-23} \mathrm{J}{ \mathrm{K}}^{-1}$.

Calculate the mean translational kinetic enegy of atoms in an ideal gas at $27°\mathrm{C}$.

The atoms in a gas have a mean translational K.E. equal to $5.0\times {10}^{-21} \mathrm{J}$. Calculate the temperature of the gas in $\mathrm{K}$ and in ${}^{\circ }\mathrm{C}$.