$A$ hydrogen cylinder is designed to withstand an internal pressure of $100 \,atm$. At $27^{\circ} C$,hydrogen is pumped into the cylinder which exerts a pressure of $20 \,atm$. At what temperature does the danger of explosion first set in? (in $K$)

The equation of an ideal gas in terms of pressure $(P)$,absolute temperature $(T)$,and density $(d)$ is:

$A$ tyre kept outside in sunlight bursts after some time because of:

$A$ monoatomic ideal gas of two moles is taken through a cyclic process starting from $1$ as shown. Given $\frac{V_2}{V_1} = 2$ and $\frac{V_4}{V_1} = 4$. The temperature at state $1$ is $T_1 = 27\,^oC$. Find the temperature at state $2$,i.e.,$T_2$ in $K$.

$A$ gas of mass $m$ undergoes expansion at a constant pressure $P$,resulting in graph $D$. Which graph will be obtained if the same gas of mass $2m$ undergoes expansion at a pressure of $P/2$?

$A$ cylinder of volume $30 \, L$ contains oxygen at an initial gauge pressure of $15 \, atm$ and a temperature of $27^{\circ}C$. After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \, atm$ and its temperature drops to $17^{\circ}C$. The mass of oxygen taken out of the cylinder is approximately ........ $kg$. (Given: $R = 8.31 \, J \, mol^{-1} K^{-1}$,molar mass of $O_2 = 32 \, g/mol$ or $32 \times 10^{-3} \, kg/mol$)