Help me solve this TAOE problem
(a)

If we want to supply \$10^{10}\$ watts of power at \$115\$ Volts then the current would have to be 
$$ I=\frac{10^{10}}{115} = 86.956 \times 10^6 Amperes$$ .

Power lost per foot = \$I^2\$ (Resistance per foot)

$$\frac{P}{foot} = I^2\frac{R}{foot} = 7.561\times 10^{!5} \times 0.05 \times 10^{-6} $$

$$= 378.071 \times 10^6 \text{ Watt per foot}$$

(b)

So all the power \$10^{10}\$ is lost in 

$$\frac{10^{10}}{78.071 \times 10^6} = 26.45 \text{ feet} \approx 8 \text{ metres}$$

(c)

The value of the Stefan–Boltzmann constant is given in SI units by

$$σ = 5.670367×10^{−8} \frac{W}{m^{2} K^{4}}$$

Emissivity of copper \$ε = 0.023\$. Note that the diameter of the wire is \$0.3048\$ metres.

Surface area of cylindrical wire 
$$A = 2\pi rh = 0.3048 \times \pi \times 8.06196 = 7.71 m^2$$

Power radiated from heated body 
$$= ε σ A T^4 = 1.0068 \times 10^{-8}T^4 = I^2R = 10^{10}$$

$$T^4 = 9.932 \times 10^{17}$$

$$T=31,569.22 \text{ Kelvin}$$

To put that into perspective, copper melts at \$1,358\$ Kelvin while the surface of the sun is \$5,778\$ Kelvin hot.