What is 'Work'?

There is a concept in thermodynamics that often causes a problem for those whose teachers present it with inadequate preparation: the concept that if a body is moved to the moon then back to its starting position, then no work has been done on the body.

Part of the problem is caused by confusing 'work' with 'effort'. Effort is a scalar - when we move something then move it back, it take us effort each way. Work is a mathematical concept, a vector - work done in one direction can undo work done the other.

When a body is moved to the moon and back, there's a lot of effort each way. There's work done too, but not on the body once the process is complete. Think of what happens: a rocket carrying the body blasts away in one direction to lift itself from the earth, then the opposite direction to slow down to the moon's surface. Then, the opposite process brings the body back to its original position. That leaves a huge amount of rocket exhaust sailing away in both directions.

'Work' has been done on the rocket exhaust alright, and most of it stays done - the exhaust keeps going forever. It's just the net work on the body that is zero.

I hope this helps :)