The mass of a hydrogen atom is $3.32 \times 10^{-27} \, kg$. If $10^{23}$ atoms per second strike a wall of area $2 \, cm^2$ at an angle of $45^{\circ}$ with the normal to the wall and reflect elastically with a speed of $10^3 \, m/s$,the pressure exerted on the wall will be: $(N/m^2)$

$A$ hot air balloon with a payload rises in the air. Assume that the balloon is spherical in shape with a diameter of $11.7 \, m$ and the mass of the balloon and the payload (without the hot air inside) is $210 \, kg$. The temperature and pressure of the outside air are $27^{\circ} C$ and $1 \, atm = 10^5 \, N/m^2$,respectively. The molar mass of dry air is $30 \, g/mol$. The temperature of the hot air inside is close to .......... $^{\circ} C$. [The gas constant,$R = 8.31 \, J K^{-1} mol^{-1}$]

An insulated container containing a monoatomic gas of molar mass $M$ is moving with a velocity $V_{0}$. If the container is suddenly stopped,find the change in temperature.

$A$ horizontal uniform glass tube of $100 \ cm$ length, sealed at both ends, contains a $10 \ cm$ mercury column in the middle. The temperature and pressure of air on either side of the mercury column are $31^{\circ} C$ and $76 \ cm$ of mercury, respectively. If the air column at one end is kept at $0^{\circ} C$ and the other end at $273^{\circ} C$, then the pressure of air which is at $0^{\circ} C$ is (in $cm$ of $Hg$):

$2.8 \ g$ of nitrogen gas $(N_2)$ is in a vessel at a temperature of $127^{\circ} C$. The amount of heat energy required to increase the rms speed of the nitrogen molecules by $41.4 \%$ is $(R = 8.31 \ J \ mol^{-1} \ K^{-1})$. (in $J$)

Two identical glass bulbs are interconnected by a thin glass tube. $A$ gas is filled in these bulbs at $N.T.P.$ If one bulb is placed in ice and another bulb is placed in a hot bath,then the pressure of the gas becomes $1.5$ times. The temperature of the hot bath will be ....... $^oC$