The graph shows the distribution of molecular velocities for the same molecule at two different temperatures (T₁ and T₂). Which temperature is greater? Explain.

Question

Graph showing molecular velocity distributions at two temperatures, T1 (blue) and T2 (red).

Accepted Answer

Hey everyone welcome back, We have to consider the graph below, comparing velocity distribution of the same molecule at different temperatures. And we need to identify which curve represents a lower temperature. So we want to recall that for or since we're comparing molecular velocity in meters per second, we're likely going to be dealing with gas molecules. And that's because we recall that gas molecules are randomly distributed in space and the speed that these gas molecules are moving at is going to be directly proportional to our temperature. And so what that means is that therefore if we increase our temperature, we would also increase our speed of our gas molecules. Or if we decrease our temperature, we would decrease the speed of our gas molecules. So because we need to find the curve that represents a lower temperature, we would look at the distribution where our lower temperature or sorry, our lower values for speed which occur around the beginning of our graph here up to like 600 m per second, we can say, and we would recognize that these lower values for speed would correspond to a lower temperature. And based on the graph below for our red curve, we have our peak occurring, Not only covering the lower values for speed, but also the higher values for speed over here, which range all the way up to around 1600 m/s, Whereas our blue peak here covers mostly the lower values for speed or molecular velocity, which range all the way up to 800 m/s. And so we would assume that the blue curve is representing a gas molecule which is moving at a slower speed due to the temperature being decreased. And so that means that if we were to label each of these curves, we can call this curve A. And we can call this curve B. We would say that therefore curve A. With its peak more towards the left, has gas molecules moving at a slower speed due to a decrease in temperature. So our final answer to complete this example is going to be that curve A represents a lower temperature affecting our gas molecules and their speed that they're moving at. So curve A is our final answer. I hope that everything that I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

The graph shows the distribution of molecular velocities for the same molecule at two different temperatures (T₁ and T₂). Which temperature is greater? Explain.

Verified Solution

Key Concepts

Kinetic Molecular Theory

Maxwell-Boltzmann Distribution

Temperature and Molecular Velocity

The graph shows the distribution of molecular velocities for the same molecule at two different temperatures (T1 and T2). Which temperature is greater? Explain.

Verified Solution

Key Concepts

Kinetic Molecular Theory

Maxwell-Boltzmann Distribution

Temperature and Molecular Velocity

The graph shows the distribution of molecular velocities for the same molecule at two different temperatures (T₁ and T₂). Which temperature is greater? Explain.