Answer:
The final pressure of the monoatomic ideal gas is 8.406 × 10⁶ pascals.
Explanation:
When a container is rigid, the process is supposed to be isochoric, that is, at constant volume. Then, the equation of state for ideal gases can be simplified into the following expression:
Where:
, - Initial and final pressures, measured in pascals.
, - Initial and final temperatures, measured in Kelvins.
In addtion, the specific heat at constant volume for monoatomic ideal gases, measured in joules per mole-Kelvin is given by:
Where:
- Ideal gas constant, measured by pascal-cubic meters per mole-Kelvin.
If , then:
And change in heat energy (), measured by joules, by:
Where:
- Molar quantity, measured in moles.
The final temperature of the monoatomic ideal gas is now cleared:
Given that , , and , the final temperature is:
The final pressure of the system is calculated by the following relationship:
If , and , the final pressure is:
The final pressure of the monoatomic ideal gas is 8.406 × 10⁶ pascals.