$\Delta_{vap} H^{\ominus}$ for water is $+40.49 \ kJ \ mol^{-1}$ at $1 \ bar$ and $100^{\circ} C$. The change in internal energy for this vaporization under the same conditions is . . . . . . . . . . $kJ \ mol^{-1}$. (Integer answer) (Given $R = 8.3 \ J \ K^{-1} \ mol^{-1}$)

$A$ sample of gas absorbs $4000 \ kJ$ of heat and the surrounding does $2000 \ J$ of work on the sample. What is the value of $\Delta U$ (in $kJ$)?

Identify from the following reactions the one that exhibits negative work done by the system.

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?

When $1 \, \text{mole}$ of monoatomic ideal gas at $T \, \text{K}$ undergoes adiabatic change under a constant external pressure of $1 \, \text{atm}$ and changes volume from $1 \, \text{L}$ to $2 \, \text{L}$,the final temperature in Kelvin would be:

$A$ cup of water at $5^{\circ}C$ (system) is placed in a microwave oven and the oven is turned on for one minute,during which the water begins to boil. Which of the following options is true?