Please tell me that if I keep my arduino uno on for 24 hours with a adapter, will it get harmed?
I have several home-brUnos and a genuine Mega 2560 that are now, or have, run 24/7 for periods of weeks to months, powered by either a USB port or a USB-type wall charger. All of them supported (or still do) a string of 2 or 3 DS18b20 digital thermo sensors and a WiFi or Bluetooth radio. None of them slept during those jobs and they all still live and continue work as well as they always have.
I have a number of Arduinos running 24/7. Nothing bad has happened to them. I suggest if you are running them from a wall-wart style adapter that you choose one supplying voltage at the lower-end of the recommended range. That is, for a Uno for example, with a 7V adapter rather than a 12V one. The reason is that the extra voltage basically has to be thrown away by the voltage regulator as heat.
An adapter supplying 9V would be OK.
An alternative is to get one of those USB chargers that supply 5V (eg. for an iPhone), and use that by running a USB cable to the USB port of the Arduino. Then the voltage regulator doesn't have to do anything at all.
I also have a number of Arduinos running 24/7 and no problems what so ever so far. Just keep the input voltage < 14-15v. because higher voltage = higher temperature (in this case). In case you need to reset your arduino in code due the long up time you can do that by connecting the reset pin to any output pin and supply logical 0 once every 24 hours for example.