$\frac{1}{24.63}$ mole of an ideal mono-atomic gas undergoes a reversible process for which $PV^3 = C$,where $C$ $(L^2 \cdot atm)$ is a constant. The gas expands from an initial volume of $1 \ L$ and an initial temperature of $300 \ K$ to a final volume of $2 \ L$. The heat lost to the surroundings by the gas is ...... $J$.

The rate of diffusion of methane at $1.0 \ atm$ pressure is twice that of another gas '$X$' kept at $1.45 \ atm$. The molecular weight of the gas '$X$' is
[$T$ kept constant]

$A$ 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 $2$.

Choose the incorrect statement from the following:

For one mole of an ideal gas,increasing the temperature from $10^{\circ} C$ to $20^{\circ} C$:

If hydrogen gas travels a distance of $10.5 \ cm$ in $5 \ s$ through a long narrow tube at a pressure of $1 \ atm$,what distance (in $cm$) will oxygen gas travel in $5 \ s$ at a pressure of $2 \ atm$?