Does powerful Core i7 PC with a 800W PSU consume more power than a weaker one on a same task?
The 800W rating on the PSU is the maximum the output it can provide.
The PSU will only draw what it needs to from the mains, and power management nowadays is pretty good at reducing the power to components when not in use, so a "high powered" machine might only consume about the same as a "low powered" machine when both are idle. It might not, depends how good the components are at reducing their individual power consumption when idle.
That said, if you have extra components (a proper graphics card vs on board, extra hard drives) or connected devices (USB devices can draw power, for example), you should expect higher idle consumption.
Also note that PSUs have an efficiency rating (often in the range of 60-80% IIRC) so have to draw more energy than the computer requires, and this efficiency tends to be worse when they are under less strain (so using your 800W PSU to power 50W is going to be less efficient than using it to power 500W).
Even if you have 800W Power supply unit , The Computer System will take power only as much needed. It doesn't mean it will always take 800W.
Additional chipsets like graphic cards, sound cards etc consumes additional power.
For your reference as you mentioned about i7
The PSU will not continually draw 800w, it will only use what it needs. However, if power bills concern you, make sure you get a green/80%+ certified devices. If you are a heavy user, these can pay for themselves very quickly.
An Intel Core I3 Has a max TDP of 73w, whilst an Intel Core I7 has between 82w and 130w
Windows and the processor has some smart features including the ability to "park" / Shutdown cores which are not currently in use in order to save power.
But to be honest, I am not sure how to answer this - a task will take longer on a Core I3 than an I7, I wonder if it is quicker to do a 20 second task on an I7 then shutdown, or the same task that may take 25 seconds on an I3 then shutdown!
I would personally go with the I7, these are all maximum values, and I would prefer the speed. In When you consider that we are talking about 20w, the cost of leaving the machine on 24x7x365 will be a matter of less than £5 a year.