Question

Assertion: The amount of work done in the isothermal expansion is greater than work done in the adiabatic system for the same final volume.
Reason: In the adiabatic expansion of a gas temperature and pressure both decrease due to decrease in internal energy of the system.
A.Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B.Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
C.Assertion is correct but Reason is incorrect.
D.Assertion is incorrect but Reason is correct.

Answer 1

The magnitude of the work for the isothermal process for the both expansion and compression is greater than the magnitude of the work for the adiabatic process.
Although the adiabatic compression work is less negative then the isothermal compression work, the amount of work depends only on its magnitude.

Complete step by step answer:
First law of thermodynamics,
$\Delta U = \Delta W + \Delta Q$
Where, $\Delta U$ is the change in internal energy, $\Delta W$ is the work and $\Delta Q$ is the heat energy conduction.
We define Work by, $\Delta W = P\Delta V$
In the isothermal expansion, the gas absorbs heat and does work to expand the volume
In an adiabatic expansion, when an ideal gas is compressed adiabatically $\left( {Q = 0} \right)$ , work done on it and its temperature increases and the gas does work and its temperature drops.
So, in the adiabatic expansion is represented by a path that follows an isotherm and the work done by the gas during that processes the area under that portion of the curve as the gas expands from Volume V1 to V2. There is no heat transfer into the gas during the expansion. so, whatever work the gas does on the environment during the expansion must come from the internal energy of the gas initially. That means that the temperature and pressure of the gas will drop from a higher value to a lower value during the expansion of the gas
Since, both Pressure and Temperature decreases hence pressure is less than the pressure of isothermal process.
So, Work done in reversible adiabatic is less.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Therefore, the correct answer is option (A).

Note: Adiabatic processes are characterized by an increase in entropy, or degree of disorder, if they are irreversible and by no change in entropy if they are reversible. Adiabatic processes cannot decrease entropy.