The speed distributions of particles in two samples, X and Y, are measured. The particles in sample X have an average speed of 600 m s−1, while those in sample Y have an average speed of 300 m s−1. The two samples are then brought into thermal contact inside a perfectly insulating, rigid container that prevents any mass exchange with the surroundings. Immediately after contact, collisions occur only at the interface between the two samples.
A computer simulation records the average particle speeds in each sample at 0.1-s intervals during the first 2 s after contact. The data are tabulated below.
Time (s) | Avg. speed in X (m s−1) | Avg. speed in Y (m s−1)
0.0 | 600 | 300
0.1 | 585 | 315
0.5 | 540 | 360
1.0 | 510 | 390
1.5 | 495 | 405
2.0 | 490 | 410
(a) Describe the trend in the average particle speeds of samples X and Y over the 2-s interval.
(b) Explain, in terms of molecular collisions, why the average speed of particles in sample X decreases while that in sample Y increases.
(c) Predict the qualitative appearance of the speed distributions for samples X and Y after a very long time has passed. Include comments on both the shape and the average value of each distribution.
(d) Use the data to argue whether the energy transfer between the two samples violates the principle of conservation of energy.
(e) Identify and correct one possible misconception a student might have after observing that the faster-moving particles in sample X slow down upon collision with slower particles in sample Y.