$A$ mixture of gas expands from $0.03\, m^3$ to $0.06\, m^3$ at a constant pressure of $1\, MPa$ and absorbs $84\, kJ$ of heat during the process. The change in internal energy of the mixture is $.....\, kJ$.

For the reaction $C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(l)$,the value of $\Delta H - \Delta U$ is:

In a closed insulated container,a liquid is stirred with a paddle to increase its temperature. Which of the following is correct?

For the reaction $C_2H_5OH_{(l)} + 3O_{2(g)} \rightarrow 2CO_{2(g)} + 3H_2O_{(l)}$,the enthalpy change $(\Delta H)$ at $27\,^oC$ is $-1366.5 \,kJ\,mol^{-1}$. What will be the value of the internal energy change $(\Delta U)$ in $kJ\,mol^{-1}$ at the same temperature?

$A$ 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 $A$:

Choose the correct option for the free expansion of an ideal gas under adiabatic conditions from the following: