This has not been very exhaustive test. I am not planning to power it by batteries but I was curious and the battery was £1 so... I tested powering the prototype using a 1200mAh USB battery, from Poundland :-P

Test:

• The battery was fully charged.
• The prototype was connected to the WiFi all the time.
• No power saving in place.
• One temperature and pressure reading every 5 seconds.
• One MQTT publish every 5 seconds.

Results:

• First though: It took several hours for only 1200mAh with a 2.4Ah charger
• It took approx 10h to empty the battery. Not too bad
• I will try with power saving measures in place