An ideal gas is taken from an initial state i to a final state f such that the ratio of its pressure to its absolute temperature is maintained constant. Determine the work done by the gas.

Step-by-step solution

Given that the ratio of pressure to absolute temperature is constant: P T = constant From the ideal gas equation, we have: PV = nRT P T = nR V Since P T is constant, nR V must also be constant. For a given amount of ideal gas, n and R are constants, which implies that the volume V of the gas remains constant throughout the process. Since the volume is constant ( dV = 0 ), the process is isochoric. The work done by the gas is given by: W = P , dV = 0