Question

How much work is done (by a battery, generator, or some other source of potential difference) in moving Avogadro's number of electrons from an initial point where the electric potential is 6.70 V to a point where the electric potential is -8.90 V? (The potential in each case is measured relative to a common reference point.)

Answer 1

W = 1.5 x 10⁶ J = 1.5 MJ

Step-by-step explanation:

First, we calculate the potential difference between the given 2 points. So, we have:

V₁ = Electric Potential at Initial Position = 6.7 V

V₂ = Electric Potential at Final Position = - 8.9 V

Therefore,

ΔV = Potential Difference = V₂ - V₁ = -8.9 V - 6.7 V = - 15.6 V

Since, we use magnitude in calculation only. Therefore,

ΔV = 15.6 V

Now, we calculate total charge:

Total Charge = q = (No. of Electrons)(Charge on 1 Electron)

where,

No. of Electrons = Avagadro's No. = 6.022 x 10²³

Charge on 1 electron = 1.6 x 10⁻¹⁹ C

Therefore,

q = (6.022 x 10²³)(1.6 x 10⁻¹⁹ C)

q = 96352 C

Now, from the definition of potential difference, we know that it is equal to the worked done on a unit charge moving it between the two points of different potentials:

ΔV = W/q

W = (ΔV )(q)

where,

W = work done = ?

W = (15.6 V)(96352 C)

W = 1.5 x 10⁶ J = 1.5 MJ