The correct relationship is

$A$ gas absorbs $100 \ J$ of heat and is simultaneously compressed by a constant external pressure of $1.5 \ atm$ from a volume of $8.0 \ L$ to $2.0 \ L$. The change in internal energy for the gas in Joules is $(1 \ L \cdot atm = 101.32 \ J)$.

In a particular reaction, $4 \text{ kJ}$ of heat is released by the system and $12 \text{ kJ}$ of work is done on the system. Calculate the $\Delta H$ and $\Delta U$.

$A$ system does $200 \, J$ of work and at the same time absorbs $150 \, J$ of heat. The magnitude of the change in internal energy is $..... \, J.$ (Nearest integer)

Given below are two statements.
Statement-$I$ : Adiabatic work done is positive when work is done on the system and internal energy of the system increases.
Statement-$II$ : No work is done during free expansion of an ideal gas.
In the light of the above statements,choose the correct answer from the options given below.

$A$ gas is allowed to expand in an insulated container against a constant external pressure of $2.5 \ atm$ from $2.5 \ L$ to $4.5 \ L$. The change in internal energy of the gas in joules is: (in $J$)