A balloonist begins a trip in a helium-filled balloon in early morning when
the temperature is \(15^{\circ} \mathrm{C}\). By mid-afternoon, the temperature
is \(30 .^{\circ} \mathrm{C}\). Assuming the pressure remains at \(1.00
\mathrm{~atm}\), for each mole of helium, calculate the following:
(a) The initial and final volumes
(b) The change in internal energy, \(\Delta E\) (Hint: Helium behaves like an
ideal gas, so \(E=\frac{3}{2} n R T,\) Be sure the units of \(R\) are consistent
with those of \(E\).)
(c) The work (w) done by the helium (in J)
(d) The heat \((q)\) transferred (in \(J\) )
(e) \(\Delta H\) for the process (in \(J\) )
(f) Explain the relationship between the answers to parts (d) and (e).