How much power dissipated in a wire?
I assume you mean "long" in terms of wavelengths, and the wavelength is just 30 cm at 1 GHz.

Calculating losses in transmission lines is a complex task. You'll have both resistive losses in the conductor(s) themselves, plus dielectric losses in the surrounding materials.

One thing you'll have to add to your model is the self-inductance of the wire, which is another way of saying that you need to know its characteristic impedance. Losses will be least if the wire is terminated at both ends by its characteristic impedance, which will eliminate standing waves on the wire.

If you have standing waves, the peak current in the wire will rise, increasing the I2R losses, and the peak voltage will also rise, increasing the dielectric losses.