Answer
$.99 \times 10^{-6} s$
Work Step by Step
We use the following equation:
$ P = e\sigma A(T^4-T_0^4)$
Thus, converting the temperatures to Kelvin and the energy to Joules, we obtain:
$ P = (.95)(5.7\times10^{-8}\times (1))(310^4 - 293^4)= 101 \ W$
Recalling that power is equal to change in energy over change in time, we adjust this equation to find:
$ \Delta t = \frac{E}{P}=\frac{100\times10^{-6}}{101}=.99\times 10^{-6}s$
