The Vrms at 100° is v and if Vrms is 2v at temperature k(282)k =?

The question seems to be related to the root mean square (RMS) voltage (Vrms) and its relationship with temperature. However, the question is not clear enough to provide a specific answer.

In general, the RMS voltage is used in physics and engineering, and it's a statistical measure of the magnitude of a varying quantity. It can be directly related to the amount of power that can be derived from an electrical signal, for example.

If we assume that the Vrms is directly proportional to the square root of the temperature (which is a common assumption in some physical systems), then we can write:

Vrms = k*sqrt(T)

where k is a proportionality constant, Vrms is the RMS voltage, and T is the temperature.

Given that Vrms = v at T = 100°, we can write:

v = k*sqrt(100)

Solving for k gives:

k = v/sqrt(100) = v/10

If Vrms = 2v at a certain temperature T, we can write:

2v = k*sqrt(T)

Substituting the expression for k from above gives:

2v = (v/10)*sqrt(T)

Solving for T gives:

T = (20v^2)/v^2 = 20

So, if the RMS voltage doubles when the temperature is 20° (in the same units as before), then the proportionality constant k would be v/10.

Please note that this is a very simplified model and may not apply to your specific situation. The relationship between RMS voltage and temperature can be much more complex in real-world systems.