Scientific analysis -- How many seconds does it take for the paper to burn?

[Carlos_Ishigami07]

TL;DR

How many seconds does it take for the paper to burn?

I have a problem: in the same anime I saw that Senku estimated the time to start burning the paper in sixty seconds, one minute and with a lens.
The data is as follows:
The lens he used has a diameter of 5 centimeters.
The solar constant, assuming it is the same as 3700 years ago, is 1362 watts per square meter.
The radiation index, or convection heat without wind, is zero.
The specific heat of paper is 1300 J / (kg * K)
The density of the paper is 900 kilograms per cubic meter.
These are the key equations:

 

[chemisttree]

What is missing is the autoignition temperature for paper.

 

[DrStupid]

These are the key equations:
View attachment 277672
View attachment 277673

No, these are not the key equations. For external heating with a lense you reather need the radiation balance. The equations above might be helpful for autoignition without additional heating. But even than there are a lot of parameters missing, e.g. the reaction order $n$, the enthalpy of reaction $\Delta H_r$ and the activation energy $E$. The pre-exponential factor (with the symbol $Z$ in the parallel thread) is not even included into the equation above.

 

[Carlos_Ishigami07]

The Z factor en the Eyring's equation is: $Z = \frac{k_{B}T}{h}$
$k_{B}$: Boltzmann's constant $1.38\times10^{-23} J/K$
$h$: Planck's constant $6.62\times10^{-34} J\cdot s$
T: Absolute temperature in Kelvin