Question on: Smith charts, power and transmission lines

[vysero]

I would simply like to know: Given a lossless transmission line with a certain characteristic impedance Z terminated in a load L. How can I go about computing the fraction of the time average incident power arriving that is dissipated in the load? Is this possible without knowing the voltage or current; is this possible only knowing L and Z?

 

[Baluncore]

I assume L is the impedance of the load.
Yes it is possible. You need to consider the impedance mismatch between Z and L, part of the energy will be transmitted, part reflected.
You need to investigate the term "Transmission Coefficient" to know the amplitude of the transmitted signal. You know L ...