Q4. Find the internal energy of 1 mol of helium at 400 K.
Helium is monatomic, f = 3: U = (3/2)RT = 1.5 × 8.314 × 400, about 4.99 kJ.
Q5. How many translational degrees of freedom does a molecule have if it is confined to move along a line? In a plane?
Along a line, one (a single coordinate fixes its position); in a plane, two.
Q6. At the same temperature, which has more internal energy per mole: helium or nitrogen (rigid)? By what ratio?
Nitrogen: (5/2)*RT against (3/2)*RT for helium, a ratio of 5 : 3. Nitrogen molecules also store energy in rotation.