Final answer:
The final temperature of the heated gas is 369.68 Kelvin. This is found using Gay-Lussac's law, which states that the pressure of a gas is directly proportional to its temperature at constant volume, and after applying the initial and final pressures and converting initial temperature to Kelvin.
Step-by-step explanation:
The student's question relates to determining the temperature of a gas after it has been heated in a sealed container. Using the ideal gas law in the form of Gay-Lussac's law for a constant volume process, which states that the pressure of a gas is directly proportional to its temperature when the volume is held constant, we can solve for the final temperature of the gas. Given the initial conditions of the gas at 19.6 °C and 3.224 atm, and the final pressure of 4.069 atm, we can use the formula:
P1/T1 = P2/T2
First, we must convert the initial temperature from Celsius to Kelvin by adding 273.15. Thus the initial temperature in Kelvin is 19.6 + 273.15 = 292.75 K.
Now, we rearrange the formula to solve for T2:
T2 = P2 × (T1 / P1)
Substituting the given values, we find:
T2 = 4.069 atm × (292.75 K / 3.224 atm)
T2 = 369.68 K
Therefore, the temperature of the heated gas is 369.68 K, which can be converted back to Celsius if needed by subtracting 273.15, yielding a final temperature of 96.53 °C.