A 100 W bulb has a tungsten filament with a total length of 1.0 m...

The power radiated by the filament is given by the Stefan-Boltzmann law:

$P = e \sigma A T^4$

The surface area of the cylindrical filament is:

$A = 2 \pi r L$

Substituting the given values:

$A = 2 \pi \times (4 \times 10^{-5}) \times 1.0 = 8 \pi \times 10^{-5} \text{ m}^2$

Substituting $A$ into the power equation:

$100 = 0.8 \times (6.0 \times 10^{-8}) \times (8 \pi \times 10^{-5}) \times T^4$

$100 = 38.4 \pi \times 10^{-13} \times T^4$

$T^4 = \dfrac{100}{38.4 \pi \times 10^{-13}}$

$T^4 = \dfrac{10^{15}}{120.64} \approx 8.29 \times 10^{12} \text{ K}^4$

Taking the fourth root:

$T \approx (8.29)^{1/4} \times 10^3 \text{ K}$

Since $1.7^4 = 8.3521$, we get:

$T \approx 1.7 \times 10^3 \text{ K} = 1700 \text{ K}$