At some level, all e-mails are bits of data being stored on a server. This implies if you delete the data, you are using less space on the server, which would mean that the server would use less power and there save energy, but that’s not really how it works.
The amount of space you have on a server is limited, and pre-allocated. It’s often in the gigabytes now a days, as many services like google also offer cloud storage for files as well out of the same server allocations. Deleting your e-mail isn’t going to significantly effect the amount of space you are using on the server, and it isn’t going to affect the amount of space allocated to you on the server either.
And storage space isn’t a major driver of power usage on a computer anyways. It’s computations, or actually making the computer doing anything that has a significant power cost. Most long term storage is non-volatile and doesn’t require power to store data anyways. This is why you don’t lose data on your hard drive when you turn your computer or phone off. In a lot of ways, telling the server to delete your e-mails probably has a higher power cost, as it needs to do all the processing required to understand what you are telling it to do, then spend the power required to flips the bits to indicate the space where that message was is free now.
And even then, the amount of power required to do that is trivial. You are probably using more power to stream 1 second of audio, simply because there is so much more data that needs to be transferred in an audio file.
Deleting an e-mail isn’t going to save power, nor is dealing with your e-mails a significant usage of power. This is completely false.
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