The gas in the cylinder under pressure p1 = 2.0 kPa was cooled from temperature T1 = 300 K

The gas in the cylinder under pressure p1 = 2.0 kPa was cooled from temperature T1 = 300 K to T2 = 270 K. What will be the pressure p2 after cooling?

p1 = 2 kPa = 2000 Pa.

T1 = 300 ° K.

T2 = 270 ° K.

p2 -?

For a constant mass of gas, the combined gas law is valid: p1 * V1 / T1 = p2 * V2 / T2.

Where p1, V1, T1 – pressure, volume, absolute temperature of the initial state of the gas, p2, V2, T2 – pressure, volume, absolute temperature of the final state of the gas.

Since the volume of gas is determined by the volume of the cylinder, the volume of gas does not change during cooling: V1 = V2.

An isochoric process of gas cooling occurs, which is described by Charles’s law: p1 / T1 = p2 / T2.

p2 = p1 * T2 / T1.

p2 = 2000 Pa * 270 ° K / 300 ° K = 1800 Pa.

Answer: the gas pressure in the cylinder will become p2 = 1800 Pa.