Question

In the given volume (V) - absolute temperature (T) graph of an ideal gas, the relation between the pressures $ P_1 $ and $ P_2 $ is

• A. \( P_1 = \frac{P_2}{2} \)
• B. \( P_1 = \frac{P_2}{3} \)
• C. \( P_1 = 3 P_2 \)
• D. \( P_1 = 2 P_2 \)

Hint:

In ideal gas law problems, remember that pressure and temperature are directly proportional at constant volume.

Answer 1

The Correct Option is A

In the volume-temperature graph for an ideal gas, the relation between the pressure and temperature for an ideal gas is given by the equation of state: \[ P \propto T \] Since the graph shows two different pressures at different temperatures, the relation between \( P_1 \) and \( P_2 \) is found to be: \[ P_1 = \frac{P_2}{2} \]
Thus, the correct relation is \( P_1 = \frac{P_2}{2} \).