(A) This is the definition of an adiabatic process.
Because the process is adiabatic, , so , so the integral of over the entire process also equals 0.
(C) By the Second Law of Thermodynamics,
where is the change in the internal energy of the gas, is the heat added to the gas, and is the work done BY the gas. Since the process is adiabatic, and . is given by
(D) As discussed in part (C),
(E) The temperature of an ideal gas is related to the internal energy by
where is the number of gas molecules, is the temperature of the gas, and is Boltzmann's constant. The internal energy of the gas is not constant (see part (C)), so the temperature cannot stay constant.
Therefore, answer (E) is correct.