A sample of 2.0 mol of an ideal monatomic gas occupies an initial volume of 0.020 m^3 at a pressure of 2.0 × 10^5 Pa.
The gas is compressed reversibly and adiabatically until its volume becomes one-fourth of the initial value.
(i) Derive, for an ideal gas, the general relation that connects pressure and volume during a reversible adiabatic change.
(ii) Using the result of part (i), determine the final pressure of the gas after the compression.
(iii) Calculate the final temperature of the gas.
(iv) Compute the magnitude of the work done by the gas during this adiabatic compression.