Entropy is the randomness of a system. At the molecular level, entropy can be de
ID: 1038172 • Letter: E
Question
Entropy is the randomness of a system. At the molecular level, entropy can be described in terms of the possible number of different arrangements of particle positions and energies, called microstates. The more microstates the system has, the greater its entropy.
Microstates depend on molecular motion. Molecules may undergo three different types of motion: translational motion, vibrational motion, and rotational motion. During translational motion, the entire molecule moves in one direction. During vibrational motion, atoms in a molecule move toward and away from one another. During rotational motion, molecules rotate or spin. The number of molecules, the space available for the molecules, and the energy available to the molecules will impact the number of microstates.
Another way of looking at entropy is that the universe is moving toward a broader distribution of energy. The universe has a constant amount of energy as stated in the first law of thermodynamics. The universe started with low entropy (concentrated in the moment before the "big bang") and the entropy has since been constantly increasing by distributing this energy. Heat distribution from high temperature to low temperature is a another example of this phenomenon.
Part A
Rank these systems in order of decreasing entropy.
Rank from highest to lowest entropy. To rank items as equivalent, overlap them.
1 mol of
helium gas at
273 K and 20 L
1/2 mol of
helium gas at
100 K and 20 L
1 mol of
carbon tetrachloride gas at
273 K and 40 L
1 mol of
chlorine gas at
273 K and 40 L
1/2 mol of
liquid helium
at 100 K
1 mol of
helium gas at
273 K and 40 L
1/2 mol of
helium gas at
273 K and 20 L
Part B
Classify each process by its individual effect on the entropy of the universe, S.
Drag the appropriate items to their respective bins.
a process run infinitesimally slowly at equilibrium and reversed to its original state
a constant composition mixture of solid and liquid water at STP (273.15 K and 1 atm)
motion of a frictionless pendulum
a bag of red marbles and a bag of green marbles dumped together on a table top
melting of ice cream from solid to liquid at 25?C
isothermal expansion of a real gas
Increases S of the universe
Does not affect S of the universe
Decreases S of the universe
Explanation / Answer
Part A
The lesser the number of microstates the smaller is the entropy. At 273K and 40L carbon tetrachloride has high entropy than chlorine and helium gas, becuase CCl4 has 5 atoms which can be arranged in different ways resulting in high number of microstates. Chlorine gas with 2 chlorine atoms is more disordered as compared helium therefore its number of microstates will be higher than helium.
Secondly, small volume further restricts the movement of gas molecules which in turn decreases the number of microstates, hence low volume decreases the entropy.
The entropy of system is directly proportion to number of moles. The entropy of 1 mol of helium gas is twice the entropy for 1/2 mol of helium gas.
Molecules with low temperature (100K) are less energetic as compared to molecules at 273K. The number of microstates decreases with decrease in temperature which result in low entropy of molecules.
In liquid state the molecules are more ordered as compared to gas state, hence the number of microstates in gas molecule will be higher which increases its entropy.
The order of entropy (High to low for the systems are as follows:
1. 1 mol carbon tetrachloride (CCl4) gas at 273K and 40L.
2. 1 mol of chlorine gas at 273K and 40L.
3. 1 mol of helium gas at 273K and 40L.
4. 1 mol of helium gas at 273K and 20L.
5. 1/2 mol of helium gas at 273K and 20L
6. 1/2 mol of helium gas at 100K and 20L.
7. 1/2 mol of liquid helium at 100K.
Part B
1. A process run infinitesimally slow at equilibrium and reversed to its original state: Does not affect entropy of the system.
2. A constant composition mixture of solid and liquid water at STP (273.15K and 1 atm): Does not affect entropy of the universe.
3. Motion of a fictionless pendulum: Does not affect entropy of the universe
4. A bag of red marbles and green marbles dumped together on the table top: Increases entropy of the universe
5. Melting of icecream from solid to liquid at 25oC: Increases entropy of the universe
6. Isothermal expansion of real gas: Increases entropy of the universe
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