In an adiabatic process,no transfer of heat takes place between the system and surroundings. Choose the correct option for the free expansion of an ideal gas under adiabatic conditions from the following:

At the $1$ bar pressure,the volume of a gas is $0.6 \ L$. If the gas receives $122 \ J$ of heat at $1$ bar pressure,the volume becomes $2 \ L$. Calculate the change in its internal energy. $(1 \ L \cdot bar = 101.32 \ J)$

$A$ gas absorbs $200 \ J$ of heat and expands by $500 \ cm^3$ against a constant external pressure of $2 \times 10^5 \ N \ m^{-2}$. What is the change in internal energy (in $J$)?

Based on the first law of thermodynamics,which one of the following is correct?

$A$ gas expands isothermally against a constant external pressure of $1 \ bar$ from $10 \ dm^3$ to $20 \ dm^3$ by absorbing $800 \ J$ of heat from the surroundings. Calculate the value of $\Delta U$. (in $J$)

Two vessels $A$ and $B$ are connected via a stopcock. Vessel $A$ is filled with a gas at a certain pressure. The entire assembly is immersed in water and allowed to reach thermal equilibrium. After opening the stopcock,the gas from vessel $A$ expands into vessel $B$,and no change in temperature is observed. Which of the following statements is true?