AIIMS 2000 Physics Pressure-Temperature Relationship MCQ Question

To solve this problem, we can use the ideal gas law, which states that $PV = nRT$. In this scenario, we can consider the initial and final states of the gas in the flask. Initially, the pressure is $P_1 = 1$ atmosphere (atmospheric pressure) and the temperature is $T_1 = 27^{\circ}C = 300 K$. When the pressure increases to $P_2 = 2.5$ atmospheres, we need to find the new temperature $T_2$. Using the ideal gas law and the fact that the number of moles (n) and the gas constant (R) remain constant, we can set up the equation: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ Rearranging gives us: $T_2 = T_1 \cdot \frac{P_2}{P_1}$ Substituting the known values: $T_2 = 300 K \cdot \frac{2.5}{1} = 300 K \cdot 2.5 = 750 K$ Therefore, the correct answer is D) 750 K. The other options are incorrect because they do not satisfy the derived equation based on the given pressures and initial temperature.