if no energy were added to the gas during the expansion could the pressure remain constant
So long as temperature remains constant the same amount of energy given to the system persists throughout its operation and therefore, theoretically, the value of k will remain constant. However, due to the derivation of pressure as perpendicular applied force and the probabilistic likelihood of collisions with other particles through collision theory, the application of force to a surface may not be infinitely constant for such values of v, but will have a limit when differentiating such values over a given time. Forcing the volume V of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure p must decrease proportionally. Conversely, reducing the volume of the gas increases the pressure. Boyle's law is used to predict the result of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas.
Boyle's law