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Here's a common question. Do you burn more calories when you're thinking a lot and thinking hard? Does thinking really burn more calories or does the exhaustion come from somewhere else? You're not the only one wondering that. Ferris Jabr from Scientific American ended up writing an interesting piece about the phenomenon. He points out that there's no denying that the brain works hard:
Although the average adult human brain weighs about 1.4 kilograms, only 2 percent of total body weight, it demands 20 percent of our resting metabolic rate (RMR)-the total amount of energy our bodies expend in one very lazy day of no activity. RMR varies from person to person depending on age, gender, size and health. If we assume an average resting metabolic rate of 1,300 calories, then the brain consumes 260 of those calories just to keep things in order. That's 10.8 calories every hour or 0.18 calories each minute.
But how much does that change when you really think hard? It's not an easy answer, and despite experiments to find that out, Jabr finds there's no firm conclusion. But what is apparent is that the increase of energy consumption are far less important than our attitude towards the mental workout:
Completing a complex crossword or sudoku puzzle on a Sunday morning does not usually ruin one's ability to focus for the rest of the day-in fact, some claim it sharpens their mental state. In short, people routinely enjoy intellectually invigorating activities without suffering mental exhaustion.

Such fatigue seems much more likely to follow sustained mental effort that we do not seek for pleasure-such as the obligatory SAT-especially when we expect that the ordeal will drain our brains. If we think an exam or puzzle will be difficult, it often will be. Studies have shown that something similar happens when people exercise and play sports: a large component of physical exhaustion is in our heads.
[Scientific American]