If $Q$ is the heat liberated from the system and $W$ is the work done on the system,then the first law of thermodynamics can be written as:

Based on the first law of thermodynamics,which one of the following is correct?

For which reaction is $\Delta H \neq \Delta U$?

In a cylinder,$1.0 \, \text{kcal}$ of heat is added to $1.2 \, \text{L}$ of $O_2$ gas at a constant pressure of $1 \, \text{atm}$. The volume changes to $1.5 \, \text{L}$. Calculate the change in internal energy $(\Delta U)$ for this process. (in $, \text{kcal}$)

$A$ gas undergoes a change from state $A$ to state $B$. In this process,the heat absorbed and work done by the gas are $5\, J$ and $8\, J$,respectively. Now,the gas is brought back to $A$ by another process during which $3\, J$ of heat is evolved. In this reverse process of $B$ to $A$:

For the reaction $CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$ at $977 \, ^\circ C$,$\Delta H = 174 \, kJ/mol$. Calculate $\Delta U$ in $kJ$.