Calculate the changes in entropy of the Universe as a result of the following processes:
((a)) A capacitor of capacitance 1μF is connected to a battery of emf. 100 V at 0∘C. (NB think carefully about what happens when a capacitor is charged from a battery.)
((b)) The same capacitor, after being charged to 100 V, is discharged through a resistor at 0∘C.
((c)) One mole of gas at 0∘C is expanded reversibly and isothermally to twice its initial volume.
((d)) One mole of gas at 0∘C is expanded reversibly and adiabatically to twice its initial volume.
((e)) The same expansion as in (d) is carried out by opening a valve to an evacuated container of equal volume.