$A$ mixture of $He$ and $CH_4$ in a molar ratio of $4:1$ is present in a container at a pressure of $20 \ bar$. Due to a hole in the container,the gas mixture leaks out. What will be the composition of the gas mixture effusing out initially (in $: 1$)?

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 ........... .

When a sample of gas is compressed at constant temperature from $15 \, atm$ to $60 \, atm$,its volume changes from $76 \, cm^3$ to $20.5 \, cm^3$. Which of the following statements are possible explanations of this behaviour?
$(1)$ The gas behaves non-ideally
$(2)$ The gas dimerises
$(3)$ The gas is adsorbed into the vessel walls

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 $400 \ K$?

The pressure exerted by a mixture of $3.2 \ g$ of methane $(CH_4)$ and $4.4 \ g$ of $CO_2$ contained in a $9 \ dm^3$ flask at $27^{\circ}C$ is: (in $atm$)

$A$ fixed mass '$m$' of a gas is subjected to a transformation of states from $K$ to $L$ to $M$ to $N$ and back to $K$ as shown in the figure.
$1.$ The succeeding operations that enable this transformation of states are:
$(A)$ Heating,cooling,heating,cooling
$(B)$ Cooling,heating,cooling,heating
$(C)$ Heating,cooling,cooling,heating
$(D)$ Cooling,heating,heating,cooling
$2.$ The pair of isochoric processes among the transformation of states is:
$(A)$ $K$ to $L$ and $L$ to $M$
$(B)$ $L$ to $M$ and $N$ to $K$
$(C)$ $L$ to $M$ and $M$ to $N$
$(D)$ $M$ to $N$ and $N$ to $K$
Give the answer for question $1$ and $2$.