Why Does Torque Of An Engine Vary With Rpm? How Is It Related To Engine Power?

In the simple language,  the derivation of the power  implies that , P=2 x 3.14 x N x T/60  which means that  power is directly proportional to the angular speed and the torque and vice verca and  now consider for the constant power P, if the porque increases the  spoeed N increases and vice verca.  All that because the torque is the product of the force and the perpendicular dist.    So, If a force is allowed to act through a distance, it is doing mechanical work. Similarly, if torque is allowed to act through a rotational distance, it is doing work. Power is the work per unit time. However, time and rotational distance are related by the angular speed where each revolution results in the circumference of the circle being travelled by the force that is generating the torque. This means that torque that is causing the angular speed to increase is doing work and the generated power may be calculated as:      POWER=TORQUE X ANGULAR SPEED    SO, ANGULAR SPEED= 2 X 3.14 X ROTATIONAL SPEED AND i.e SPEED N

The torque of an engine is due to the pressure acting on the top of the piston.
This pressure is related to the piston speed, moving in the cylinder, and then in turn to RPM. Piston speed influences the quantity and the path of air, coming into the cylinder, and the quantity and path of burnt gas leaving the piston cylinder.
On the top of the cylinder there are valves, they function by introducing air and releasing burnt gas.
The sequence of the opening and closing of the valves, is also related to RPM.
The last parameter influencing the torque, is fuel quantity,
that is injected into the cylinder, and its path, this parameter is also influenced by RPM, in terms of the filling of the cylinder.
The torque varies in this way, and the torque is related to the power of the engine, by multiplying it (Nm , Newton metres)
by the angular speed of the engine (RPM x 3.14 /60) and the power is obtained in watts.