Assume that the centre of the sun consists of gases whose average molecular weight is $2$. The density and pressure of the gases are $1.3 \mathrm{g} {\mathrm{mL}}^{-1}$ and $1.12\times {10}^9 \mathrm{atm}$, respectively. Find the temperature. If $\mathrm{T} = \mathrm{y} \times {10}^7 \mathrm{K}$ then $y$ is:

A volume of a gas weighing $8 \mathrm{g}$ was allowed to expand at a constant temperature until the pressure of the gas reduced to one-half of its former value. It was found that $500 \mathrm{mL}$ of the gas weighed $1.25 \mathrm{g}$. Determine the initial density of the gas in $\mathrm{g} {\mathrm{L}}^{-1}$.

An ideal gas with density of $3.0 \mathrm{g}/\mathrm{L}$ has pressure of $675 \mathrm{mm} \mathrm{Hg}$ at $25°\mathrm{C}$. What is the $\mathrm{rms}$ speed $\left(\text{in} \mathrm{m}/\mathrm{s}\right)$of the molecules of this gas? $\left(1 \mathrm{atm}=101325 \mathrm{Pa}=760 \mathrm{mm} \mathrm{Hg}\right)$

Round off your answer to the nearest integer.

An $\mathrm{He}$ atom at $25°\mathrm{C}$ is released from the surface of the earth to travel upwards. Assuming that it undergoes no collisions with other molecules, how high will it travel before coming to rest? The height is $\mathrm{a}\times {10}^4 \mathrm{m}$, find the value of $\text{'}\mathrm{a}\text{'}$.

The escape velocity is given by:

$\mathrm{v}=\sqrt{2\mathrm{gr}}$

where, $\mathrm{r}=6.37\times {10}^6 \mathrm{m}$ for the earth. At what temperature will the $\mathrm{RMS}$ velocity of an ${\mathrm{H}}_2$ molecule attain the escape velocity? The temperature is $\mathrm{a}\times {10}^4 \mathrm{K}.$ Find the value of $\text{'}\mathrm{a}\text{'}$ correct up to two places of decimal.

At $27°\mathrm{C}$, hydrogen leaks through a tiny hole in a vessel for $20 \min$. Another unknown gas at the same temperature and pressure as that of ${\mathrm{H}}_2$ leaks through the same hole for $20 \min$. After the effusion of the gases, the mixture exerts a pressure of $6 \mathrm{atm}$. The hydrogen content of the mixture is $0.7 \mathrm{mol}$. If the volume of the container is $3 \mathrm{L}$, what is the molecular weight of the unknown gas? $\left(\mathrm{R}=0.0821 \mathrm{atm} \mathrm{L} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}\right)$

Round-off your answer to the nearest integer.