Which of the following is true for the value of $\Delta H - \Delta U$ at constant volume?

The volume of $100 \ L$ of gas increases to $120 \ L$ at a constant temperature and an external pressure of $10 \ bar$. Calculate the work done by the system. [Given: $1 \ L \ bar = 24.21 \ cal$] (in $cal$)

What is the work done when $2 \text{ mole}$ of an ideal gas are expanded isothermally and reversibly from $5 \text{ m}^{3}$ to $10 \text{ m}^{3}$ at $300 \text{ K}$ (in $\text{ kJ}$)? $(R=8.314 \text{ J K}^{-1} \text{ mol}^{-1})$

The work done during the expansion of a gas from a volume of $4 \ dm^3$ to $6 \ dm^3$ against a constant external pressure of $3 \ atm$ is $(1 \ L \ atm = 101.32 \ J)$ $...... \ J$

Consider the following statements:
$(1)$ Joule-Thomson experiment is isoenthalpic as well as adiabatic.
$(2)$ $A$ negative value of $\mu_{JT}$ (Joule-Thomson coefficient) corresponds to warming of a gas on expansion.
$(3)$ The temperature at which neither cooling nor heating effect is observed is known as inversion temperature.
Which of the above statements are correct?

Fill in the blanks:
$(i)$ The change in heat energy during a chemical reaction at constant volume is called .......
$(ii)$ During a ....... process,there is no absorption or evolution of heat.
$(iii)$ The equation $\Delta G = \Delta H - T \Delta S$ was proposed by .......