Quiz 1 #7

Volume: $\Delta S = nR\ln \frac{V_{2}}{V_{1}}$
Temperature: $\Delta S = nC\ln \frac{T_{2}}{T_{1}}$

melissapasao1B
Posts: 14
Joined: Wed Sep 21, 2016 2:56 pm

Quiz 1 #7

Can someone explain #7 to me? I understand the effects that pressure and volume have on entropy, however, when I read the processes provided, I get confused on how to relate their effects on entropy.

Thanks!

hafsa_zulfiqar_1j
Posts: 28
Joined: Fri Jul 22, 2016 3:00 am

Re: Quiz 1 #7

So for question 7: first recall that entropy is a measure of disorder, so the more positions there are for atoms and molecules to move in the more disorder there is, which means a higher entropy.

Part 1 says that the pressure of 1 mole of gas is allowed to double isothermally. Pressure and volume are inversely related, and because this system is under constant temperature, that means doubling the pressure will lead to the volume being decreased to half of what it originally was, thus leading to less positions for the gas molecules to move in and an overall decrease in entropy.

Part 2 says that carbon dioxide is allowed to expand isothermally to 10 times its original volume. In this scenario, because the volume is being increased by a factor of 10 there are more positions available to the gas molecules which would lead to an increase in entropy.

Part 3 says that the temperature of 1 mole of helium is increased 25 degrees at constant pressure. Entropy is defined as q (heat) divided by T (temperature) so an increase in temperature would mean a larger denominator and a smaller entropy value or a decrease in entropy.

Part 4 says that nitrogen gas is compressed isothermally to half its original volume. Once again, less volume means less positions for the gas atoms and molecules to move in, meaning a decrease in entropy.

Part 5 says that a glass of water loses 100 J of energy reversibly at 30 degrees Celsius. Entropy increases when temperature increases because there is a larger supply of energy and thus greater disorder because the thermal motion of molecules is increased. In this scenario, energy is lost, so the thermal motion is decreased, which means less disorder and a decrease in entropy.

Therefore, the answer to #7 (which of these processes lead to an increase in entropy) is processes #2 and 3.

Hope this helps!

hafsa_zulfiqar_1j
Posts: 28
Joined: Fri Jul 22, 2016 3:00 am

Re: Quiz 1 #7

Oh wait, sorry follow up: correction. For process 3, I explained incorrectly. Because the system is under a constant pressure, raising the temperature would lead to greater thermal motion and greater disorder and thus an increase in entropy. I apologize for the confusion, I misread the question.