Question

6. (10 pts) Polarized water. Water is a polar molecule; one side has a slight positive charge and one side has a slight negative charge. You wish to do an experiment where all the water molecules are lined up in the same direction (say, positively-charged sides are all 'up" and negatively charged sides are all "down")... but water is in random thermal motion, so on average the orientations of the molecules are all random. The mean thermal energy of a water molecule is about EhermalkBT- 42e-21 J İf the energy of the water molecules in the "correct" direction compared to molecules in the opposite direction is ~3X lower than Edbermal (i.e., is about 1.2e-20 J) then the water will be mostly oriented in the desired direction. You decide to do this by putting the water between the plates of a capacitor and charging up the plates. a. What voltage must you charge the capacitor up to in order for the energy of the right-side-up water molecule (see figure) to be 3 Ethermal 1.2e-20 J less than the wrong-side-up molecule? Capacitor Plate Model water molecule Wrong side up molecule Q-0.36a.-6-20 C Distance- 1A-1e-10m 1.0 cm Capacitor Plate

Answer 1

6]

a] Work done by a capacitor = W = (1/2)Q²/C

Here, work done by the capacitor = energy in the correct direction = 1.2 x 10^-20 J

Q = 6 x 10^-20 C

therefore, Capacitance will be:

C = 1.5 x 10^-19 F

now use, Q = CV

=> V = Q/C = 0.4 volts

this is the required voltage.