$A$ gas cylinder can withstand a pressure of $15 \ atm$. At $27 \ ^oC$,the pressure in the cylinder is $12 \ atm$. Up to what temperature in $^oC$ will the cylinder not burst?

$2 \times 10^6$ molecules of $N_2$ gas enter into a vessel having a volume of $400 \, mL$ at $400 \, K$ temperature. Find the pressure in $atm$ and $bar$. $[R = 0.082 \, L \, atm \, mol^{-1} \, K^{-1}]$,$[1 \, atm = 1.013 \, bar]$

For an ideal gas,the number of moles per litre in terms of its pressure $P$,gas constant $R$,and temperature $T$ is:

At $25 \, ^\circ C$ temperature and $760 \, mm \, Hg$ pressure,the volume of a gas is $600 \, mL$. Calculate the pressure when the volume of this gas becomes $640 \, mL$ at $10 \, ^\circ C$ temperature. Use the ideal gas equation: $\frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}$

At $27^{\circ} C$,$1 \ L$ of $H_2$ with a pressure of $1 \ bar$ is mixed with $2 \ L$ of $O_2$ with a pressure of $2 \ bar$ in a $10 \ L$ flask. What is the pressure exerted by the gaseous mixture in $bar$? (Assume $H_2$ and $O_2$ as ideal gases)

The $log \, T$ vs $log \, V$ curve is plotted for an ideal gas as shown. Which of the following is true for the gas?