When a system absorbs $8 \ kJ$ of heat and does $2.2 \ kJ$ of work on the surroundings,calculate the internal energy change. (in $kJ$)

What is the final temperature of $0.10 \ mol$ monoatomic ideal gas that performs $75 \ cal$ of work adiabatically if the initial temperature is $227 \ ^\circ C$? (Use $R = 2 \ cal \cdot K^{-1} \cdot mol^{-1}$)

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 $...\,kJ$

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

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 which of the following reactions is $\Delta H = \Delta E$?