If by "polymerisation of coding region" you mean "mRNA synthesis", then honestly, there is no fixed answer to this question (for eukaryotes, certainly).

Many genes have enormous lengths of intronic sequence, all of which must be transcribed, only to then be spliced down to a comparatively small mRNA for translation. Dystrophin, for example, is 2.3 million bases long, but is spliced down to ~14,000 (i.e. 99.5% of the transcribed nucleotides are spliced out and recycled).

Here transcription clearly requires a greater energy input on a 1:1 mRNA:protein basis, whereas other shorter (or intronless) genes might be closer to parity.

However you also need to factor in energy requirements for recruitment of initiation factors, unwinding of the transcriptional start site, scanning, abortive initiation, etc, which will also vary from gene to gene. Some genes are permissive, other are less so.

You also need to factor similar variables to translation: targeting of mRNA, recruitment of translation initiation factors, unwinding and scanning of 5' UTR, etc.

And finally, this all assumes you are comparing mRNA and protein on a 1:1 basis, which is entirely inaccurate. A single mRNA can be translated many, many times, so a large energy investment in one transcript might ultimately pale in comparison to the vast energy investment in making 10,000 proteins from that one transcript. Alternatively, a single mRNA might be degraded without ever being translated even once (some 'immediate early' genes are transcribed continuously, 'just in case', but then degraded if not needed).

If you want to know (more generally) 'what uses more energy in a cell, transcription or translation?', then the answer is almost always translation: translation (i.e. protein synthesis) consumes about 50% of the energy budget of a proliferating cell. Ribosomes are not very efficient, and cells contain LOTS of them (~80-85% of cellular RNA is just ribosomes). They are always in use.

I wouldn't worry about asking questions like this, by the way: it's an excellent question and exposes quite how many complexities there are to even such an ostensibly simple consideration.

Hi..

To calculate the total energy required for transcription, you would need to multiply the energy required to synthesize each nucleotide by the number of nucleotides in the coding region.

It's worth noting that transcription and translation are complex processes that involve multiple steps and require the input of various types of energy. The figures I provided are just rough estimates of the overall energy requirements of these processes. If you would like more detailed information on the energy requirements of transcription and translation, I recommend consulting a biochemistry textbook or scientific journal.

Regards

Another point to consider is that each mRNA molecule can be translated many times. So calculating the energy of one mRNA vs one protein molecule is one thing, but one mRNA vs 100 protein molecules is something else entirely.

Looking at it globally though, the act of translation in a metabolically active cells is usually the highest consumer of energy.