$A$ gas is allowed to expand in a well-insulated container against a constant external pressure of $2.5 \ atm$ from an initial volume of $2.50 \ L$ to a final volume of $4.50 \ L$. The change in internal energy $\Delta U$ of the gas in joules will be .............. $J$.

Two moles of an ideal gas are allowed to expand from a volume of $10 \ dm^3$ to $2 \ m^3$ at $300 \ K$ against a pressure of $101.325 \ kPa$. Calculate the work done. (in $kJ$)

Identify the state function among the following.

For water $\Delta_{vap} H = 41 \ kJ \ mol^{-1}$ at $373 \ K$ and $1 \ bar$ pressure. Assuming that water vapour is an ideal gas that occupies a much larger volume than liquid water,the internal energy change during evaporation of water is $...... \ kJ \ mol^{-1}$.
[Use: $R = 8.3 \ J \ mol^{-1} \ K^{-1}$]

Calculate the internal energy change of one mole of an ideal gas during an adiabatic free expansion process from a volume of $2 \ L$ to $5 \ L$.

For the reaction $CH_3COOH_{(l)} + 2O_{2(g)} \rightleftharpoons 2CO_{2(g)} + 2H_2O_{(l)}$ at $25\,^{\circ}C$ and $1\,atm$ pressure,$\Delta H = -874\,kJ.$ Then the change in internal energy $(\Delta E)$ is $...\,kJ$