Question

The volume of a sample of air in a cylinder with

a movable piston is 2.0 L at a pressure P1 , as
shown in the diagram above. The volume is
increased to 5.0 L as the temperature is held
constant. The pressure of the air in the cylinder is
now P2 . What effect do the volume and pressure
changes have on the average kinetic energy of the
molecules in the sample?
(A) The average kinetic energy increases.
(B) The average kinetic energy decreases.
(C) The average kinetic energy stays the same.
(D) It cannot be determined how the kinetic
energy is affected without knowing P1
and P2 .

Answer 1

The average kinetic energy of a gas is directly proportional to its temperature, according to the kinetic theory of gases. This means that if the temperature is held constant, the average kinetic energy of the gas molecules will also be constant, regardless of any changes in volume or pressure.

Therefore, the correct answer is (C) the average kinetic energy stays the same.

Answer 2

I used Chat GPT to answer the question here is the answer

Assuming the gas behaves ideally, the answer is (C) The average kinetic energy stays the same.

According to the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. If the temperature is held constant, then nR is also constant. Therefore, for a given amount of gas, if V increases, P must decrease (and vice versa) to maintain the same value of PV.

The average kinetic energy of gas molecules is proportional to temperature, so if the temperature is held constant, the average kinetic energy of the gas molecules stays the same. The changes in volume and pressure only affect the density and distribution of the gas molecules, but not their average kinetic energy.