(5 pts) Is superfluid 4He a BEC? Liquid 4He (a boson) undergoes a sharp transition from a normal fluid to a superfluid2 at T = 2.2 K. Is this transition a Bose-Einstein condensation? Its not immediately obvious, because (a) liquid helium is a strongly-interacting system, not a gas, and (b) it can be shown that a perfectly ideal bose gas (with no interactions at all) is not a superfluid. One piece of evidence relating helium superfluidity to BEC is that T is roughly similar to the BEC transition temperature Tc computed for an ideal gas at the same number density N/V . Show this by computing Tc and comparing to T. Notes: In notes 10.7 the number density Nc/T above which BEC occurs is given. When (as in this problem) N/V is given, this same equation can be inverted to give the temperature Tc below which BEC occurs. The molar volume of liquid 4He near T is 27.6 cm3

1. (5 pts) Is superfluid 4He a BEC? Liquid 4He (a boson) undergoes a sharp transition from a normal fluid to a superfluid 2 at T=2.2K. Is this transition a Bose-Einstein condensation? It's not immediately obvious, because (a) liquid helium is a strongly-interacting system, not a gas, and (b) it can be shown that a perfectly ideal bose gas (with no interactions at all) is not a superfluid. One piece of evidence relating helium superfluidity to BEC is that T is roughly similar to the BEC transition temperature Tc computed for an ideal gas at the same number density N/V. Show this by computing Tc and comparing to T. Notes: - In notes 10.7 the number density Nc/T above which BEC occurs is given. When (as in this problem) N/V is given, this same equation can be inverted to give the temperature Tc below which BEC occurs. - The molar volume of liquid 4He near T is 27.6cm3