PVT Behavior of an Ideal Gas

#179 / Thermo Easy

Consider a 5 L tank of nitrogen gas with a pressure of 1.0 atm. If the tank is compressed to a volume of 2 L, calculate the new pressure.

Expand Hint

$$$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$$

where $$P$$ is pressure, $$V$$ is volume, and $$T$$ is temperature.

Hint 2

Because temperate is not given in the problem statement, we can ignore that specific section of the equation. Therefore:

$$$P_1V_1=P_2V_2$$$

For an ideal gas:

$$$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$$

where $$P$$ is pressure, $$V$$ is volume, and $$T$$ is temperature.

Because temperature is not given in the problem statement, ignore that variable from the equation. Therefore:

$$$P_1V_1=P_2V_2$$$

$$$1atm\cdot 5L=P_2\cdot 2L$$$

$$$P_2=\frac{1atm(5L)}{2L}=2.5\:atm$$$

2.5 atm

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