Chapter 42, Problem 1P

To determine

The temperature of the helium at which it would condense.

Answer to Problem 1P

The temperature of the helium is $10\text{K}$.

Explanation of Solution

Write the expression to calculate the energy of the helium.

  $E=\frac{3}{2}kT$

Here, E is the energy, k is the Boltzmann constant and T is temperature.

Substitute $1\text{meV}$ for E and $1.38\times {10}^{-23}\text{J}/\text{K}$ for k in the above equation to calculate T.

  $\begin{array}{c}\frac{3}{2}\left(1.38\times {10}^{-23}\text{J}/\text{K}\right)T=1\text{meV}\left(\frac{{10}^{-3}\text{eV}}{1\text{meV}}\right)\left(\frac{1.602\times {10}^{-19}\text{J}}{1\text{eV}}\right)\\ T=\left(\frac{2}{3}\right)\left(11.6\text{K}\right)\\ =7.74\text{K}\\ ~10\text{K}\end{array}$

Conclusion:

Therefore, the temperature of the helium is $10\text{K}$.