If a power utility were able to replace an existing 500 kV transmission line with one operating at 1 MV, it would change the amount of heat produced in the transmission line to

It would change the amount of heat produced in the transmission line to four times the previous value.

Explanation:

Given;

initial voltage in the transmission line, V₁ = 500 kV = 500,000 V

Final voltage in the transmission line, V₂ = 1 MV = 1,000,000

The power lost in the transmission line due to heat is given by;

Power lost in the first wire;

Power lost in the second wire

Keeping the resistance constant, we will have the following equation;

Therefore, it would change the amount of heat produced in the transmission line to four times the previous value.