There is no change in internal energy of an ideal gas when it undergoes

Two cylinders $A$ and $B$ of equal capacity are connected to each other via a stopcock. $A$ contains a gas at standard temperature and pressure. $B$ is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened. Answer the following :
$(a)$ What is the final pressure of the gas in $A$ and $B$?
$(b)$ What is the change in internal energy of the gas?
$(c)$ What is the change in the temperature of the gas?
$(d)$ Do the intermediate states of the system (before settling to the final equilibrium state) lie on its $P-V-T$ surface?

$A$ container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure $P$ and temperature $T$,whereas the other part is completely evacuated. If the valve is suddenly opened,the pressure and temperature of the gas will be

$Assertion :$ In free expansion of an ideal gas,the entropy increases.
$Reason :$ Entropy increases in all natural processes.

Following are statements of a few processes taking place in nature:
$I$. Free expansion of a gas
$II$. The combustion of a mixture of petrol and air ignited by a spark
$III$. The leaking of gas from the kitchen cylinder
$IV$. The transfer of heat from one heated part of a liquid to the other colder part
Which amongst these processes are irreversible in nature?

Consider the given diagram. An ideal gas is contained in a chamber (left) of volume $V$ and is at an absolute temperature $T$. It is allowed to rush freely into the right chamber of volume $V$ which is initially vacuum. The whole system is thermally isolated. What will be the final temperature once the equilibrium has been attained?