$A$ gaseous sample expands from $200 \, cm^3$ to $500 \, cm^3$ against a constant external pressure of $750 \, torr$ while absorbing $1.5 \, J$ of heat. What is the change in internal energy of the system in $J$? $(1 \, atm \cdot L = 101.3 \, J)$

For the reaction $FeCO_{3(s)} \to FeO_{(s)} + CO_{2(g)}$,$\Delta H = 82.8 \ kJ$ at $25 \ ^oC$. What is $\Delta U$ at $25 \ ^oC$ in $kJ$?

Which of the following processes exhibits an increase in internal energy?

An engine absorbs heat $Q_1$ at temperature $T_1$ and heat $Q_2$ at temperature $T_2$. The work done by the engine is given as $W = Q_1 + Q_2$. Which of the following statements is correct?

Given below are two statements.
Statement-$I$ : Adiabatic work done is positive when work is done on the system and internal energy of the system increases.
Statement-$II$ : No work is done during free expansion of an ideal gas.
In the light of the above statements,choose the correct answer from the options given below.

The change in internal energy equals