A rigid container holds 4.00 mol of a monatomic ideal gas that has temperature 300 K. The initial pressure of the gas is 6.00 * 104 Pa. What is the pressure after 6000 J of heat energy is added to the gas?

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.

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