The relation between $\Delta H$ and $\Delta U$ for the reaction $2 SO_{3(g)} \longrightarrow 2 SO_{2(g)} + O_{2(g)}$ is:

$A$ piston filled with $0.04\, mol$ of an ideal gas expands reversibly from $50.0\, mL$ to $375\, mL$ at a constant temperature of $37\, ^oC$. It absorbs $208\, J$ of heat in this process. The value of $q$ and $w$ for the process will be: $(R = 8.314\, J / mol\, K)$ $(\ln 7.5 = 2.01)$

Calculate the internal energy change of one mole of an ideal gas during an adiabatic free expansion process from a volume of $2 \ L$ to $5 \ L$.

Which of the following is the correct mathematical expression for the first law of thermodynamics?

$A$ gas expands from a volume of $4 \ L$ to $14 \ L$ against a constant external pressure of $1 \ atm$ in a cylinder with a frictionless piston. During this process,the gas absorbs $800 \ J$ of heat from the surroundings. Calculate the change in internal energy $\Delta E$ in $J$. (in $.7$)

Which of the following is the correct expression of the first law of thermodynamics for an isothermal process?