Question

For an adiabatic process, which of the following relations is correct?
A.$\delta E = 0$
B.$P\delta V = 0$
C.$q = 0$
D.$q = +w$

Answer 1

Hint:
An adiabatic process is a process that occurs without transferring heat or mass between a thermodynamic system and its surroundings. These changes are usually accompanied by changes in temperature.

Complete step by step answer:
An adiabatic process is a thermodynamic process in which there is no exchange of heat from the system to its surrounding neither during expansion nor during compression. An adiabatic process either can be reversible or irreversible.
Following are some of the conditions for the adiabatic process to take place:
The process must be carried out quickly so that there is a sufficient amount of time for heat transfer to take place.
The system must be perfectly insulated from the surroundings.

Now, according to the first law of thermodynamics: total energy of an isolated system is always conserved.
$\implies \delta E = q + w$
where, $\delta E = internal energy$,
$q = heat$, and
$w = work$

For an adiabatic process, the heat exchange between the system and the surrounding is zero i.e., $q = 0$. Putting the value of q in the first law of thermodynamics, we get,
$\delta E = 0 + w$
$\implies \delta E = w$

Thus, looking at the options, options (a), (b) and (d) are incorrect. Thus, the correct option is option (c).

Note:
Only for free expansion, since ${P}_{ext} = 0$, then the work done, w = 0.
Thus, in that condition only, for an adiabatic process, q = 0, $\delta v = 0$ and $\delta T = 0$.