At $400 \ K$, an ideal gas is enclosed in a $0.5 \ m^3$ vessel at a pressure of $203 \ kPa$. What is the change in temperature required (in $K$), if it occupies a volume of $0.2 \ m^3$ under a pressure of $304 \ kPa$? (Nearest integer)

An open vessel at $27\,^{\circ}C$ is heated until two-fifths of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant,the temperature to which the vessel has been heated is:

$28 \ g$ of $N_2$ gas occupies $10 \ L$ volume at $2.46 \ atm$ pressure. Calculate the temperature in $K$.

$A$ gas cylinder contains cooking gas at $14.9 \ atm$ pressure. The pressure gauge of the cylinder reads $12 \ atm$ at $27 \ ^oC$. If the cylinder bursts due to a sudden fire in the building,at what temperature in $^oC$ will the cylinder burst?

$A$ plot of volume $(V)$ of the gas versus temperature ($T$ in $K$) is shown below. Which of the following options is correct for the plot?

At a constant temperature,two different gases $G_1$ and $G_2$ are kept in separate flasks. The molar mass of $G_2$ is three times that of $G_1$,while the density of $G_1$ is two times that of $G_2$. What is the ratio of the pressure exerted by $G_2$ to that of $G_1$ in their respective flasks?