An ideal gas is in a 1.00-m³ box at a gauge pressure of 210 kPa and a temperature of 295 K.It is then allowed to undergo free expansion into an adjacent 2.00-m³ box,so the total volume is now 3.00 m³.Find the new gauge pressure once a new equilibrium is reached.The pressure outside the box is standard atmospheric pressure,101.3 kPa.

Question

Quizplus · Accepted Answer

The initial state of the gas can be represented by:

P1 = 210 kPa
V1 = 1.00 m3
T1 = 295 K

The final state of the gas after free expansion can be represented by:

P2 = ?
V2 = 3.00 m3
T2 = 295 K

Because the expansion is free (i.e. no work is done), the internal energy of the gas remains the same. Therefore, we can use the ideal gas law to find the new pressure:

P1V1/T1 = P2V2/T2

Solving for P2, we get:

P2 = (P1V1/T1) * (T2/V2) = (210 kPa * 1.00 m3/295 K) * (295 K/3.00 m3) = 2.47 kPa

This is the gauge pressure inside the box. To find the absolute pressure, we need to add the atmospheric pressure outside the box:

Pabs = Pgage + Patm = 2.47 kPa + 101.3 kPa = 103.8 kPa ≈ 104 kPa

Therefore, the correct answer is (A) 2.47 kPa.

An Ideal Gas Is in a 1