A fixed mass of an ideal gas is taken separately through the three operations described below. (The initial state is the same for all operations.)
(a) (i) The gas is slowly compressed while its temperature is kept constant by placing the cylinder in a large water bath.
(b) (ii) The gas is allowed to expand by heating it gently while the piston is kept free so that the pressure inside the cylinder never changes.
(c) (iii) The gas is quickly compressed adiabatically so that its temperature rises and the pressure increases at the same time.
(d) For each operation, identify the thermodynamic process involved (name only).
(e) Explain qualitatively, with suitable reasoning, how the other two state variables (pressure, volume or temperature) vary during each operation.
(f) Draw a rough sketch of the expected P–V graph for each of the above processes on the same axes and label them clearly.