The total pressure of a gas and a few drops of water in a container is $830 \, mm$. If the temperature of the container is decreased by $1 \%$,the new pressure is $............ \, mm$. The water vapor pressures at the two temperatures are $30 \, mm$ and $25 \, mm$ respectively.

Under the same $P$ and $T$,which of the following pairs of gases will diffuse at the same rate through a small jet?

$A$ 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 $2$.

Two flasks $I$ and $II$ shown below are connected by a valve of negligible volume. When the valve is opened,the final pressure of the system in bar is $x \times 10^{-2}$. The value of $x$ is $.....$ . (Integer answer) [Assume-Ideal gas; $1 \, bar = 10^{5} \, Pa$; Molar mass of $N_{2} = 28.0 \, g \, mol^{-1}$; $R = 8.31 \, J \, mol^{-1} \, K^{-1}$]

When equal volumes of helium and neon at same temperature and pressure are mixed,the ratio $C_p: C_V$ of the mixture equals

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 $\text{ K}$)?