Question

Two Cylinders $A$ and $B$ of equal capacity are connected to each other via a stop cock. $A$ contains an ideal gas at standard temperature and pressure, $B$ is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened.The process is

• A. $\text{Isochoric}$
• B. $\text{Isobaric}$
• C. $\text{Isothermal}$
• D. $\text{Adiabatic}$

Answer 1

The correct option is D $\text{Adiabatic}$

Free expansion i.e. expansion against vacuum is adiabatic in nature for all type of gases. It should be noted that temprature final temperature is equal to initial temperature for ideal gases.Read more on Sarthaks.com - https://www.sarthaks.com/905868/two-cylinders-a-and-b-of-equal-capacity-are-connected-to-each-other-via-a-stop-cock

For the thermally insulated system, $dq=0$, and when cock removed, due to free expansion $dw=0$.
As we know, $dq=du+dw$, so $du=0$.

Following are the essential conditions for the adiabatic process to take place. The system must be perfectly insulated from the surrounding. The process must be carried out quickly so that there is a sufficient amount of time for heat transfer to take place.
According to question both conditions satisfied so process will be adiabatic.