$A$ box of $1 \, L$ capacity is divided into two equal parts by a thin partition,which are filled with $2 \, g$ of $H_2$ and $16 \, g$ of $CH_4$ respectively. The temperature of each part is $T$. The pressure in each part is $P$. If the partition is removed,the total pressure will be:

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 $\text{ K}$)?

Which of the following statements is correct?

$A$ 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 $2$.

$A$ and $B$ are ideal gases. The molecular weights of $A$ and $B$ are in the ratio of $1: 4$. The pressure of a gas mixture containing equal weights of $A$ and $B$ is $P \text{ atm}$. What is the partial pressure (in $\text{atm}$) of $B$ in the mixture?

$A$ gas sample of $1.47 \ L$ was collected over water at $30 \ ^\circ C$ and $744 \ mm \ Hg$ pressure. If the weight of the gas is $1.98 \ g$,what is the molar mass of the gas? (Assume the vapor pressure of water at $30 \ ^\circ C$ is $31.8 \ mm \ Hg$)