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

$A$ gas is allowed to expand in an insulated container against a constant external pressure of $10 \ atm$ from an initial volume $4.2 \ L$ to $5.2 \ L$. The change in internal energy $\Delta E$ of the gas will be $:-$

Two vessels $A$ and $B$ are connected via a stopcock. Vessel $A$ is filled with a gas at a certain pressure. The entire assembly is immersed in water and allowed to reach thermal equilibrium. After opening the stopcock,the gas from vessel $A$ expands into vessel $B$,and no change in temperature is observed. Which of the following statements is true?

If a system absorbs $30 \ kJ$ of heat and performs $12 \ kJ$ of work on the surroundings,what is the increase in internal energy of the system (in $kJ$)?

For the reaction $PCl_{5(g)} \to PCl_{3(g)} + Cl_{2(g)}$,which of the following relations is correct?

An ideal gas expands against a constant external pressure of $2 \ bar$ from $5 \ L$ to $8 \ L$ and absorbs $10 \ kJ$ of heat. What is $\Delta U$ of the system (in $J$)?