$\frac{1}{2}$ mole of helium gas is contained in a container at $S.T.P.$ The heat energy needed to double the pressure of the gas,keeping the volume constant (specific heat of the gas $= 3 \; J \; g^{-1} \; K^{-1}$) is ...... $J$.

In saloons,there is always a characteristic smell due to the ammonia-based chemicals used in hair dyes and other products. Assume the initial concentration of ammonia molecules to be $1000 \text{ molecules}/m^3$. Due to air ventilation,the number of molecules leaving in one minute is one-tenth of the molecules present at the start of that minute. How long will it take for the concentration of ammonia molecules to reach $1 \text{ molecule}/m^3$?

The same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1:4$,then:
$A.$ The $r.m.s.$ velocity of gas molecules in the two vessels will be the same.
$B.$ The ratio of pressure in these vessels will be $1:4$.
$C.$ The ratio of pressure will be $1:1$.
$D.$ The $r.m.s.$ velocity of gas molecules in the two vessels will be in the ratio of $1:4$.

$A$ gas is filled in the cylinder shown in the figure. The two pistons are joined by a string. If the gas is heated,the pistons will

The figure shows a plot of $PV/T$ versus $P$ for $1.00 \times 10^{-3} \; kg$ of oxygen gas at two different temperatures.
$(a)$ What does the dotted plot signify?
$(b)$ Which is true: $T_{1} > T_{2}$ or $T_{1} < T_{2}$?
$(c)$ What is the value of $PV/T$ where the curves meet on the $y$-axis?
$(d)$ If we obtained similar plots for $1.00 \times 10^{-3} \; kg$ of hydrogen,would we get the same value of $PV/T$ at the point where the curves meet on the $y$-axis? If not,what mass of hydrogen yields the same value of $PV/T$ (for the low-pressure,high-temperature region of the plot)?
(Molecular mass of $H_{2} = 2.02 \; u$,of $O_{2} = 32.0 \; u$,$R = 8.31 \; J \; mol^{-1} K^{-1}$.)

One mole of an ideal gas undergoes a linear process as shown in the figure below. Its temperature expressed as a function of volume $V$ is