A \(0.320-\mathrm{kg}\) piston seals a chamber that contains \(7.55 \times 10^{24}\) helium atoms initially at \(2.00^{\circ} \mathrm{C}\). The piston is free to move vertically, but it is originally held fixed in place with the chamber volume at \(0.250 \mathrm{~m}^{3}\). When the piston is released, the chamber volume immediately increases as the piston moves upward. At the instant when the piston has moved \(0.320 \mathrm{~m}\) from its initial position, its velocity is \(43.5 \mathrm{~mm} / \mathrm{s}\) upward. The air pressure in the room is \(1.00 \mathrm{~atm}\), and the piston has a circular cross-section and a radius of \(0.200 \mathrm{~m}\). What is the final temperature of the gas if the expansion is \((a)\) isentropic and \((b)\) isothermal?