I asked this question a long while ago, but I never got an answer to whether mental exhaustion can be measured. If mental exhaustion could be measured, it would mean that I would have a way of knowing the performance I can get out of my brain in a day. I would be able to know what is best for refilling my brain with energy (maybe TV is your best option after all...;) ) As far as I understand, different parts of the brain gets used for different purposes, so they should get exhausted at different times, so the measuring would have to be on specific regions of the brain or performance of the brain in various fields.
Can mental exhaustion be measured?
mental exhaustion
A sleep study by Van Dongen et al (2003) uses three metrics to measure the effects of fatigue due to sleep loss.  The first is cognitive throughput:A serial addition/subtraction task was included in the assessment  battery to measure cognitive throughput. The serial  addition/subtraction task is a subject-paced task requiring the  completion of 50 mental arithmetic trials. The average number of  correct responses per min was used as a neurobehavioral assay of  cognitive throughput performance.Second, alertness / vigilance (response time to stimuli):The neurobehavioral assessment battery included a psychomotor  vigilance task to measure behavioral alertness. The psychomotor  vigilance task (PVT) is a sustained-attention reaction time task with  a random inter-stimulus interval of 210 s. Lapses (reaction times  greater than 500 ms) were counted per 10 min test bout as a measure of  performance.Third, memory:The neurobehavioral assessment battery also included a computerized  digit symbol substitution task to measure working memory. This  subject-paced task involves the matching of digits (09) to symbols  (circle, triangle, etc.). The number of correct responses in 1.5 min  was counted to measure working memory performance.The metrics ought to be effective for measuring mental performance due to fatigue whatever the cause of fatigue might be.ReferencesVan Dongen, H.P.A., Maislin, G., Mullington, J.M., Dinges, D.F. & others (2003). The cumulative cost of additional wakefulness: dose-response effects on neurobehavioral functions and sleep physiology from chronic sleep restriction and total sleep deprivation. SLEEP-NEW YORK THEN WESTCHESTER-, 26, 117-129.