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?

The volume of a gas at $STP$ is $1.5 \ L$. When $300 \ J$ of heat is supplied to it at $1 \ atm$ pressure,its volume becomes $2 \ L$. What is the value of $\Delta U$ in $J$ for this process? $(1 \ L \cdot atm = 101 \ J)$

For the reaction $3O_{2(g)} \rightarrow 2O_{3(g)}$,the value of $\Delta U - \Delta H$ is equal to .....

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?

Calculate the change in internal energy $(\Delta U)$ if $\Delta H = -92.2\, kJ$,$P = 40\, atm$,and $\Delta V = -1\, L$.

When $1 \ mole$ of gas is heated at constant volume,the temperature rises from $273 \ K$ to $546 \ K$. If heat supplied to the gas is $x \ J$,then find the correct statement from the following.