Physics

Problem

- A flask of volume

300.0 \times 10^{-6}

m³ contains air at a pressure of

5.00 \times 10^5

Pa and a temperature of

27.0^\circ\text{C}

. The flask loses molecules at a rate of

3.00 \times 10^{19}

per second. Estimate how long it takes for the pressure in the flask to fall to half its original value. (Assume that the temperature of the air remains constant during this time.)

Intuitive explanation

The key is recognizing that pressure depends on the number of gas molecules in a fixed volume at constant temperature. Using the ideal gas law, you can relate the initial and final number of molecules to the pressure ratio, then divide by the loss rate to find the time needed. This transforms a gas behavior problem into a straightforward rate calculation.

Intuitive explanation

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