Two moles of an ideal monoatomic gas are allowed to expand adiabatically and reversibly from $300 \ K$ to $200 \ K$. The work done in the system is $... \ kJ$ $(C_V = 12.5 \ J/K/mol)$.

$A$ gas expands from a volume of $4 \ L$ to $14 \ L$ against a constant external pressure of $1 \ atm$ in a cylinder with a frictionless piston. During this process,the gas absorbs $800 \ J$ of heat from the surroundings. Calculate the change in internal energy $\Delta E$ in $J$. (in $.7$)

$5 \, mol$ of an ideal gas expands isothermally and irreversibly from a pressure of $10 \, atm$ to $1 \, atm$ against a constant external pressure of $1 \, atm$. The work done $(w_{irr})$ at $300 \, K$ is:

$A$ 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 $J$)

The correct option for free expansion of an ideal gas under adiabatic condition is

$A$ gas present in a cylinder expands against a constant pressure of $1 \, atm$ from a volume of $2 \, L$ to a volume of $6 \, L$. In doing so,it absorbs $800 \, J$ of heat from the surroundings. The change in internal energy of the process is ..... $J$.