Question

The P-V diagram of a diatomic ideal gas going under cyclic process as shown in the figure. The work done during an adiabatic process CD is (use \[\gamma \] =1.4):

(1) - 500 J
(2) - 400 J
(3) 400 J
(4) 200 J

Answer 1

Hint: An adiabatic process defines a process in thermodynamics where transferring of energy takes place without the transfer of mass or heat to the surrounding.

Formula used:
The formula for the work done is,
\[W = \dfrac{{{p_f}{v_f} - {p_i}{v_i}}}{{1 - \gamma }}\]
Here, W is work done, \[{p_f}\] is the final pressure, \[{p_i}\] is the initial pressure, \[{v_f}\] is the final volume and \[{v_i}\] is the initial volume.

Complete Step by Step Solution:
The Given diagram represents the adiabatic process of an ideal gas. From the graph, \[{p_i}\]is 100 N/m2 and \[{p_f}\]is 200 N/m2 . And \[{v_f}\]is 3 and \[{v_i}\]is 4 and \[\gamma \]is 1.4.
Putting all the above values in the formula of W.
So, work done in adiabatic process is,
\[\] \[{W_{CD}} = \dfrac{{200 \times 3 - 4 \times 100}}{{1 - 1.4}}\]
\[{W_{CD}} = \dfrac{{600 - 400}}{{ - 0.4}}\]
\[{W_{CD}} = - 500\,J\]
Hence, the work done in the given adiabatic process is -500 J. Therefore, option (1) is right

Additional Information:
Thermodynamics defines the studying of relations between work, energy, heat and temperature. The different thermodynamic law explains how the change of energy of a system takes place and whether the system has the ability to perform important work on the surroundings.

Note: There is the possibility of both reversibility or irreversibility of an adiabatic process. The necessary conditions required for the adiabatic process: (a)Perfect insulation of the system from the surrounding (b) The process should happen quickly so that there is enough time for the taking place of heat transfer.