To a very good approximation, we can assume that the air in a room is an ideal gas consisting mostly of nitrogen molecules, with a molecular weight of 28 Dalton = 28 g/mol. A. We can use the average kinetic energy formula to find the average value of the velocity squared; we will call the "average speed" the square root of this value, or Vawe (v). Determine the average speed of a nitrogen molecule, at T = 300 K and P = 1 atm (10 Pa).
B. Assume that a nitrogen molecule is moving in the horizontal (+x) direction at the speed that you calculated in part (A). This molecule collides with the right wall of the container and rebounds back, in the x direction, with the same speed. What is the change in the momentum of the nitrogen molecule?
C. If there was one such collision per second, what would be the magnitude of the average force exerted by the molecule on the wall?
D. For the gas to exert a pressure of 1 atm what should be the average force on a 1m x 1m wall due to collisions by the gas molecules?
E. Compare your answers in (C) and (D) above to estimate the number of collisions per second necessary to add up to 1 atm of pressure on a Imx Im wall.
In the derivation of the pressure exerted by a gas, we only included the kinetic energy of the gas molecules. We neglected the gravitational potential energy completely, in the following question, why we did so.
F. Suppose the room was 5 m tall, and consider a system consisting of a nitrogen molecule and the earth. Compute the ratio between the change in gravitational potential energy of the system if the nitrogen molecule falls from the ceiling of the room to the floor of the room. and the average kinetic energy of a nitrogen molecule, Delta ug / (x)