Bose gas — UPSC Physics Optional IFoS 2024 Paper I

The volume of a mole of liquid \text{He}^4 is 27 \times 10^{-6}\text{ m}^3 and the mass of a \text{He}^4 atom is 6.65 \times 10^{-27}\text{ kg}. Assuming that liquid \text{He}^4 is an ideal Bose gas, calculate (i) the concentration of boson in this volume. (ii) Bose temperature.