why does the voltage of a galvanic cell becomes zero at equilibrium?

 A galvanic cell's voltage drops to zero at equilibrium because the electrical potential of the two half-cells becomes perfectly equal. The cell produces voltage by allowing a spontaneous redox reaction to occur. At equilibrium, the forward and reverse reactions proceed at the exact same rate, meaning no net work can be done and no electrons can flow through the external circuit.  As the cell operates, products are formed and reactants are consumed, driving the reaction quotient Q toward the equilibrium constant K. At chemical equilibrium, Q = K.

Because there is no longer a driving force for the reaction, the Gibbs free energy change Delta G equals zero. Consequently, the cell potential Ecell drops to exactly '0'volts.

Mathematicaly we know that

Delta G = -nFEcell = -(nF)V = - (total charge transfered) x Voltage = work done by the cell = loss in its potential energy.

so Delta G = 0 is possible only when Ecell = 0

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4 major effects of inserting a dielectric slab inside a parallel plate capacitor

 

(i) Electric filed DECREASES by a factor K

Enew = Eold/K 

(ii) Capacitance INCREASES by a factor K

Cnew = KCold

(iii)

Voltage DECREASES by a factor K

Vnew = Vold/K

(iv) 

PERMITIVITY of capacitor INCREASES by a factor K

ε = Kε₀

Is the number of all INTO functions from the set {1, 2, 3, ..... n} to itself equal to all number of MANY to ONE fuctions?

Yes,  the number of all into functions from the set {1, 2, 3, .... n} to itself is exactly equal to the number of many-to-one functions for all positive integers n, as both are quantified by the formula n^n - n!

Find the number of all INTO functions from the set {1, 2, 3, ..... n} to itself

 

Is a ONE to MANY relation a function?

 

Is a MANY to MANY relation a function?

 

find the number of all BIJECTIVE functions from the set {1, 2, 3, ..... n} to itself