Final answer:
To find the final pressure of a gas sample that's been heated from 100 K to 400 K, we use Gay-Lussac's law. The initial pressure is 80 kPa, and by applying the formula P2 = P1 × (T2 / T1), we determine the final pressure to be 320 kPa.
Step-by-step explanation:
The question requires the application of the ideal gas law in a scenario where the temperature of a gas sample is changed, and one needs to find the final pressure assuming volume and the number of moles of the gas remain constant. According to Gay-Lussac's law, which is a specific case of the ideal gas law, the pressure of a gas is directly proportional to its temperature (measured in Kelvin) when volume and the quantity of gas are held constant.
To find the final pressure when the temperature changes, we can apply the relationship P1/T1 = P2/T2, where P1 and T1 are initial pressure and temperature, and P2 and T2 are final pressure and temperature respectively. Substituting the values from the question, we have:
- P1 = 80 kPa (initial pressure)
- T1 = 100 K (initial temperature)
- T2 = 400 K (final temperature)
We need to solve for P2 (final pressure):
P2 = P1 × (T2 / T1) = 80 kPa × (400 K / 100 K) = 80 kPa × 4 = 320 kPa.
The final pressure of the gas after being heated to 400 K is 320 kPa.