[Four-digit Integer] An unspecified quantity of an ideal gas was at initial pressure of 5 atm and te — States of Matter and Gaseous State Chemistry Question
Question
[Four-digit Integer] An unspecified quantity of an ideal gas was at initial pressure of 5 atm and temperature of 303 K. The gas is expanded at 303 K until the volume has increased by 60% of the initial value. Next, the quantity of the gas in the vessel is increased by 20% of the initial value while the volume is maintained constant. Finally, the temperature is adjusted at constant volume until the gas pressure is again 5 atm. What is the final temperature, in kelvin?
💡 Solution & Explanation
Initial: $P_1=5$ atm, $V_1$, $n_1$, $T=303$ K. After isothermal expansion to $1.6V_1$: $P_2=5/1.6=3.125$ atm. Add 20\% gas at const V and T: $n_3=1.2n_1$, $P_3=3.75$ atm. Heat to restore $P=5$ atm: $T_4 = \frac{P_4 V_3}{n_3 R} = \frac{5\times1.6V_1}{1.2n_1 R} = \frac{8}{1.2}\times\frac{303}{5} = 404$ K. Answer: $\boxed{0404}$