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 $...\,kJ$

When a system expands under adiabatic conditions,what happens to its internal energy?

Assertion : For a reaction $2NH_{3(g)} \to N_{2(g)} + 3H_{2(g)}$ ; $\Delta H > \Delta E$.
Reason : Enthalpy change is always greater than internal energy change.

$A$ system gives out $x \ J$ of heat and does $y \ J$ of work on its surroundings. What is the internal energy change?

$A$ gas expands against a variable pressure given by $P = \frac{20}{V}$ ($P$ in $atm$ and $V$ in $L$). During expansion from volume of $1 \ L$ to $10 \ L$,the gas undergoes an increase in internal energy of $400 \ J$. How much heat is absorbed by gas during expansion (in $J$)? (Given: $1 \ L \cdot atm = 101.3 \ J$)

$C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l)$. The enthalpy change $(\Delta H)$ for the above reaction at $27^{\circ}C$ is $-1366.5 \text{ kJ mol}^{-1}$. Calculate the internal energy change $(\Delta U)$ for the same reaction at this temperature.