# Equation for number of crosslinked polymer strand in rubber

#### semc

I am doing an experiment to estimate N, the number of crosslinked polymer strand in a piece of rectangular rubber. To do this, I attached weights to the rubber and measure the extension of the rubber when subject to the force. However, I found two equations that can be used to find N and they give different results hopefully someone can tell me which equation I should use.

Firstly, $$F=N(kb)T(\frac{x+X}{X^2}-\frac{X}{(X+x)^2})$$ where (kb) is the boltzmann constant, T the temperature, X is the original length and x is the total length of the rubber after the weight is added.

The second equation is k=(3NkbT)/X2 where k is the spring constant of the spring. I have totally no clue where this equation is derived from.

Thanks

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