Which one among the following is the correct option for the relationship between $C_{P}$ and $C_{V}$ for one mole of an ideal gas?

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?

When the temperature of $2$ moles of an ideal gas is increased by $20^{\circ} C$ at constant pressure,find the work involved in the process. (in $R$)

Two moles of an ideal gas are expanded isothermally from $15 \ dm^3$ to $20 \ dm^3$. If the amount of work done is $-6 \ dm^3 \ bar$,find the external pressure needed to obtain this work.

Among the following, which are extensive variables?

In thermodynamics,which one of the following is not an intensive property?