I know this is going off topic, but I'm intrigued as to why I'm wrong.
Because it is far too simplistic. So.. it's now Saturday and I have a little time
There are two aspects to power consumption for laptops - idling power and power when computing. You get extra battery life by making idling power consumption as low as possible. This is done by hardware on chip which calculates thousands of times a second how fast the clocks should be running on each part of the chip and scales the clocks back. On my Sandy Bridge desktop, the idle speed is 1600MHz. On my Sandy Bridge laptop, it is 800MHz - if the CPU is not clock gated to 0Hz (where nothing is running), each CPU runs at this speed until it needs more power where the clocks ramp higher up to their maximum value. This clock ramping is done on a CPU by CPU basis (so you may have the CPUs on one die running at different speeds). Battery life is generally proportional to how low these clocks go and how often the CPU is scheduled to run. Newer processors do more and better clock scaling so power goes lower, even though the clocks are the same. There is also an effect from the Operating System - my understanding is that Microsoft have done a lot of work here on Windows 8. Apple have always been good at this which is why Macbooks have relatively long battery life. Fundamentally battery life is dominated by the idling power as the clock scaling takes care of only running the chip fast enough for the task in hand - and it does it many thousands of times a second!
Intel CPUs also have something called Turbo Boost whereby the clocks are ramped above the nominal maximum. The amount they can boost by is limited and depends on the number of CPUs active - the fewer that are active, the higher those fewer processors are clocked. Looking at the fastest quad-core i7's in each lineup you have:
- i7-2700K: 95W TDP, 3.5GHz, 1/2/3/4 turbo (i.e. max speed for 1, 2, 3 and 4 cores flat out is 3.9GHz, 3.8GHz, 3.7GHz and 3.6GHz respectively)
- i7-3770K: 77W TDP, 3.5GHz, 2/3/4/4 turbo (i.e. max speed for 1, 2, 3 and 4 cores flat out is 3.9GHz, 3.9GHz, 3.8GHz and 3.7GHz respectively)
- i7-4790K: 88W TDP, 4GHz, 2/3/4/4 turbo (i.e. max speed for 1, 2, 3 and 4 cores flat out is 4.4GHz, 4.4GHz, 4.3GHz and 4.2GHz respectively)
So Sandy->Ivy = less power, slightly faster maximum speed (3.6GHz vs 3.7GHz), whilst Ivy->Haswell gives the same power (77/3.5 * 4 = 88) with higher maximum speed which is what you'd expect - Sandy->Ivy is a process shrink so things should get faster and use less power whilst Ivy->Haswell is a design change but same process (so similar power) but improved design has allowed them to get faster clocks (4.2GHz vs 3.7GHz). You will also notice there are normally a range of processors that are pretty similar but run at different speeds. These will be speed-binned at manufacture and the faster processors sold at a premium.
But this isn't the total story. There is also hardware that is measuring the total power being used. It also checks the total thermal envelope of the processor and if it is reaching the limits, it will also scale clocks back until things get better. This is known as throttling and the CPU automatically does it if needed. Low TDP parts tend to have lower clock speeds to reduce the maximum power dissipation. Why do this? Why not just put a high performance CPU in and let clock scaling take care of things? Yes, you do get reduced maximum performance, but more interesting for laptop designers is reduced thermal stresses on the laptop chassis. If you have a 100W processor in a laptop, not only is the battery life going to be pants when it's running flat out, you have 100+ watts to get rid of from your beautifully designed enclosure and most of it will try going into the owner's lap!
But clocking isn't the only thing that matters.
You may know Intel tinker between related architectures and do significant redesign between pairs of designs (their tick-tock design cycle if you want to google it). You can tell paired designs as they have similar names Sandy Bridge & Ivy Bridge, Haswell & Broadwell etc. The first of these is the major redesign, the second of these is process shrink (which pipecleans the process for the next re-design). Process shrink means smaller die so less power, it should also mean faster clocks, but getting the heat out of the chip is becoming a major problem, so often things are not increased but left pretty much as-is clockwise. To compare clock for clock performance, the measure instructions per cycle (often written IPC) is used. This is effectively a measure of how much work you can get done in single clock cycle. The more work you can get done in one cycle, the fewer cycles you have to expend to do the same amount of work. Between iterations of the same architecture, Intel might do some minor tweaks. I think they modified the number and type of execution units in the CPU between Sandy and Ivy which means that each new generation tends to ramp IPCs. Sandy->Ivy saw an ~10% IPC improvement which translates to ~10% better performance per MHz. Looking at the numbers above, if all 4 cores are 100% loaded (and ignoring hyperthreading) then the i7-2600K performance is effectively 3.6GHz x 4 = 14.4 whilst the Ivy is 3.7GHz x 4 x 1.1 = 16.28. In other words, the Ivy processor, even though it runs at the
same nominal clock speed is approximately 13% faster. It's also dissipating 19% less power too. The same type of gains will be made between Ivy and Haswell....
If you have higher IPC, you can get the same amount of work done in a shorter time. Conversely, you can also do that work in the same amount of time but at a lower clock speed which has the
added benefit of reducing the maximum power consumption. It is very unlikely to alter the idle power consumption as clock scaling takes care of that. Given laptop design is always a compromise it allows manufacturers to have a still perfomant laptop that uses less power whilst still being cheap enough for consumers to buy.... Bottom line is that the driver on power consumption/battery life is only very loosely related to headline GHz (try defining what f and V are in the equation above given the discussion above and knowing similar processes are ongoing on voltage scaling too).