Question 12
1 pts
In a system the mass is kept constant. The initial temperature of the system is \( 131^{\circ} \mathrm{C} \) and the volume is \( 7.1 \mathrm{~L} \). If the temperature changes to \( 31.1^{\circ} \mathrm{C} \), the pressure to \( 29.4 \mathrm{~atm} \), and the volume changes to \( 15.7 \mathrm{~L} \), what was the original pressure?
Answer
Solve for the initial pressure, \(P_1\): \(P_1 = \frac{P_2V_2T_1}{T_2V_1}\)
Step 1 ：Using the ideal gas law: \(PV = nRT\)
Step 2 ：Since mass is constant and the gas is the same, we can relate the initial state and final state through their volumes, temperatures, and pressures: \(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\)
Step 3 ：Solve for the initial pressure, \(P_1\): \(P_1 = \frac{P_2V_2T_1}{T_2V_1}\)
