When $2 \ L$ of an ideal gas expands isothermally into a vacuum to a total volume of $6 \ L$,what is the change in internal energy in $J$? (Nearest integer)

At a definite temperature,for which of the following reactions will the value of $(\Delta E - \Delta H)$ be maximum?

$A$ gas is allowed to expand against a constant external pressure of $2.5 \ bar$ from an initial volume of $2.5 \ L$ to a final volume of $4.5 \ L$. What is the amount of work done (in $J$)?

Calculate the constant external pressure required to expand $2$ moles of an ideal gas from volume $15 \ dm^{3}$ to $20 \ dm^{3}$ if the amount of work done is $-600 \ J$. (in $bar$)

Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures $T_1$ and $T_2$ $(T_1 < T_2)$. The correct graphical depiction of the dependence of work done $(|w|)$ on the final volume $(\ln V)$ is:

Prove the relationship between $C_p$ and $C_v$ for an ideal gas.