Do coaxial rotors provide twice the amount of lift given same diameter and RPM?
What about the engine? Even if engine power was doubled, the coaxial rotor won't produce double the lift.
Airfoils don't like stacking neighbors.
This double wing above (biplane) produced about 120% lift, not 200%.
Using the biplane above to illustrate a point, between the wings the pressure will neither be high enough for the upper wing, nor low enough for the lower wing.
In a biplane aircraft, two wings are placed one above the other. Each provides part of the lift, although they are not able to produce twice as much lift as a single wing of similar size and shape because the upper and the lower are working on nearly the same portion of the atmosphere and thus interfere with each other's behavior.
For the same engine output, we're looking at ~10% increase in lift.
Because the coaxial rotor does not require an anti-torque device such as a tail rotor, Fenestron, or Notar, a coaxial rotor helicopter requires about 10% less power than a single rotor/tail rotor helicopter.
For the same rotor diameter and power the coax will lift approximately 11% more weight. This equates to 30% greater useful load, which means more payload or fuel. The coax helicopter can hover at a 6000 ft higher altitude, or at a higher temperature (avxaircraft.com).
Yes they can give twice the amount of lift if blade angle of attack is a variable, but require more power to do so. Momentum theory predicts:
a 28% power penalty on this configuration, when compared to running the two rotors in isolation, when the two rotors are operated at equal thrust.
a 22% power penalty when the two rotors are operated at equal rotor torque.
a 41% power penalty when the rotors have no vertical separation.
Experiments have shown a power penalty that is less than predicted by momentum theory: 16%.
Source: Principles of Helicopter Aerodynamics, J. Gordon Leishman, section 2.15.1