The mathematical equation of the first law of thermodynamics for an isochoric process is:

When $x \ kJ$ heat is provided to a system,work equivalent to $y \ J$ is done on it. What is the internal energy change during this operation?

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

The $\Delta U^{\theta}$ of combustion of methane is $-X \ kJ \ mol^{-1}.$ The value of $\Delta H^{\theta}$ is

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?

For an isothermal reversible expansion process,the value of $q$ can be calculated by the expression