AIIMS 2018 Physics Ideal Gas Law MCQ Question

To determine the temperature at which the vessel will explode at 15 atm, we can use the ideal gas law, which states that $PV = nRT$. Given that pressure and temperature are directly proportional at constant volume and amount of gas, we can set up a ratio: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$. Substituting the known values, $\frac{10 \, \text{atm}}{300 \, \text{K}} = \frac{15 \, \text{atm}}{T_2}$, we find $T_2 = 450 \, \text{K}$.

Options B (500 K), C (550 K), and D (600 K) are incorrect because they do not satisfy the ratio derived from the ideal gas law, indicating that they do not correspond to the conditions under which the vessel would explode at the specified pressures.