Identify the correct statements from the following:
$(A)$ The compressibility factor $(Z)$ for an ideal gas is $1$.
$(B)$ Uranium isotopes (${ }^{235}U$ and ${ }^{238}U$) are separated by converting them into $UF_6$ vapours.
$(C)$ Decrease in temperature increases the kinetic energy of gas molecules.

What is the temperature at which the kinetic energy of $0.3 \text{ moles}$ of helium is equal to the kinetic energy of $0.4 \text{ moles}$ of argon at $400 \text{ K}$ (in $\text{ K}$)?

Choose the incorrect statement from the following:

Fill in the blanks:
$(1)$ Each line of the graph of pressure versus temperature (in Kelvin) at a specific molar volume is called ........... .
$(2)$ $A$ gas that strictly follows Boyle's,Charles's,and Avogadro's laws is called ........... .
$(3)$ The ratio of the most probable speed to the average speed is ........... .
$(4)$ The ratio of $U_{rms}$ to $U_{mp}$ is ........... .

At $STP$,a closed vessel contains $1 \ mole$ each of $He$ and $CH_4$. Through a small hole,$2 \ L$ of $He$ and $1 \ L$ of $CH_4$ escaped from the vessel in '$t$' minutes. What are the mole fractions of $He$ and $CH_4$ respectively remaining in the vessel? (Assume $He$ and $CH_4$ as ideal gases. At $STP$,one mole of an ideal gas occupies $22.4 \ L$ of volume.)

The variation of pressure with volume of a gas at different temperatures can be graphically represented as shown in the figure. On the basis of this graph,answer the following questions:
$(i)$ How will the volume of a gas change if its pressure is increased at constant temperature?
$(ii)$ At a constant pressure,how will the volume of a gas change if the temperature is increased from $200 \ K$ to $400 \ K$?