The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at $47^{\circ} \mathrm{C}$ is (Molecular weight of hydrogen and oxygen molecules are 2 and 32 respectively)

A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is (Molecular wt. of $\mathrm{O}_2 \& \mathrm{H}_2$ is 32 and 2 respectively)

The P-V graph of an ideal gas, cycle is shown. The adiabatic process is described by the region

Railway track is made of steel segments separated by small gaps to allow for linear expansion. The segment of track is 10 m long when laid at temperature $17^{\circ} \mathrm{C}$. The maximum temperature that can be reached is $45^{\circ} \mathrm{C}$. Increase in length of the segment of railway track is ' $x$ ' $\times 10^{-5} \mathrm{~m}$. The value of ' $x$ ' is $\left(\alpha_{\text {steel }}=\right.$ $\left.1.2 \times 10^{-5} /{ }^{\circ} \mathrm{C}\right)$