Welby H. answered • 09/02/21
Chemistry PhD student w/ Specialties in Math & Sciences
Answer: Average Kinetic Energy will decrease when Temperature is decreased but volume is increased
Looking at the 2 conditions separately first:
How does average KE change as a function of temperature? We know that the temperature is directly proportional to the average KE from this following equation: KEavg = 3⁄2RT. This means that if the temperature increases, average KE will also increase, and vice versa. So, with regards to temperature, lowering the temperature will result in a decreased average Kinetic Energy.
How does average KE change as a function of volume? We know that volume is indirectly related to pressure through Boyle's Law. So, when there is an increase in the volume, the pressure will decrease and vice versa. We can relate pressure with average kinetic energy through Bernoulli's Principle which states that pressure of a gas or liquid is directly proportional to the velocity of the gas or liquid. Following the logic and putting it all together: by increasing the volume, there will be a corresponding decrease in the pressure, and by decreasing the pressure, there will be a corresponding decrease in the average kinetic energy. Therefore, increasing the volume of the system will result in a decreased average kinetic energy.
On their own, each method changing the system conditions (lower temp & increase volume) will result in a decrease in kinetic energy on their own. Therefore, putting the two together, we can see that by lowering the temperature AND increasing the volume, the average kinetic energy will must be lowered in the process.
