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It looks like you have already calculated the energy required to raise the temperature of 50 kg to the boiling point. It is significantly higher than the amount of energy in a bolt of lightning, so the steps after that are not necessary. You can look at the units to guess that $\Delta T=\frac{E}{Cm},$ where $C$ is the specific heat, $m$ is the mass, and $E$ ...


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I'm just learning this myself, but for the the first one, the thermal state I think just means that if you throw any field in the resulting space-time, it will immediately acquire the specified temperature. In Hawking's original calculation, he shows that this radiation will be dominated by the massless, lowest-spin particles available, which in our universe ...


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The best way to numerically work with continuous phase transitions is to study observables that have a vanishing length dimension (or mass dimension in the language of QFT). Take for example the Binder's cumulant ($\langle m^4\rangle/\langle m^2\rangle^2$ modulo factors of 3 and constants, where $m$ is the order parameter) or the correlation length scaled by ...



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