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Experiment: Thermodynamics – Second Law, a homebased experiment
By John Wang, Arizona State University, New College of Interdisciplinary Arts and Sciences.
Purpose :
In this lab, we will exam the cooling processes of hot water and validate the second law of thermodynamics.
Introduction :
Entropy is a measure of the numbers of ways the energy can be distributed in a system of particles (molecules,
atoms, or ions). Particles in a system at equilibrium have the same average energy. However, at a given instant
of time, particle most likely have different amount of energy. One particle may have certain amount of energy at
one instant, and at next, it could have more or less. Depends on the energy the particle has, it will able to access
different energy levels. The total amount of energy will determine what energy levels are accessible to particles.
Mathematically Ludwig Boltzmann expressed entropy S, as:
S = k ln( W )
Where k is the Boltzmann constant = 1.38 x 10
J/K. W is the numbers of ways the energy can be distributed in
a system of particles
The Second Law of Thermodynamics states that entropy, or the amount of disorder in the universe, increases each
time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—
usually in the form of heat— This heat energy can temporarily increase the speed of molecules it encounters. As
such, the more energy that a system loses to its surroundings, the less ordered and the more random the
surroundings becomes.
Entropy and the Second Law of Thermodynamics describe a wide range of occurrences in nature and engineering.
A refrigerator is essentially a heat pump and removes heat from one location at a lower temperature, the heat
source, and transfers it to another location, the heat sink, at a higher temperature. According to the second law,
heat cannot spontaneously flow from a colder location to a hotter one. Thus, work, or energy, is required for
refrigeration. A campfire is another example of entropy change in real life. The solid wood used as fuel burns and
turns into a disordered pile of ash. In addition, water molecules and carbon dioxide gas are released. The atoms
in the vapors spread out in an expanding cloud, with infinite disordered arrangements. Thus, the entropy changes
from burning wood is always positive. The released heat from the burning woods heats up the surrounding and
makes the entropy of the surroundings increase, therefore, the entropy of the universe increases. That is why
burning wood is a spontaneous Process.
Thermodynamic second law can also be demonstrated in a classic food web. Herbivores harvest chemical energy
from plants and release heat and carbon dioxide into the environment. Carnivores harvest the chemical energy
produced by herbivores—with only a fraction of it representing the original radiant energy from the sun—and
also release heat energy with carbon dioxide into their surroundings. As a result, the heat energy and other
metabolic by-products released at each stage of the food web have increased its entropy.
Think about gas trapped in a container with known volume, pressure and temperature as the system. The gas
molecules can have an enormous number of possible configurations. If the container is opened, the gas molecules
escape, and the number of configurations increases dramatically, essentially approaching infinity. If in the gas
expansion process, there is no energy exchange between the gas molecules and its surrounding, the system become
the universe. Thus, ΔS, or the change in entropy for the universe is greater than zero. Thus, the gas expansion
process is spontaneous.
Similarly, entropy also increases when hot water is left at room temperature and allowed to cool down. In this
experiment, we will explore how to measure the change in entropy of the universe during a cooling experiment.
And calculate the free energy change for the water in the cooling process.
Before learning how to do the experiment and gather data, let's learn some laws and equations that allow us to
calculate temperature change and increase in entropy during cooling experiments. Newton's Law of Cooling states
that the rate of temperature change of an object is proportional to the difference between its own temperature and
the temperature of the surroundings.
𝑠
Where T is the temperature of the object, T s
is the temperature of the surroundings. Using calculus, this
relationship can be converted into this equation,
𝑠
0
𝑠
−𝑘𝑡
where lower case t represents time, T s
denotes temperature of the surroundings, T 0
is the initial temperature of
the object, T(t) is the temperature of the object at time t, and k is a constant that depends on the characteristics of
the object and its surroundings.
Using this equation, one can calculate the temperature of a cooling system at any time if all the other variables
are known. This equation also shows that temperature is an exponential function of time. Thus, when a hot object,
like a glass of hot water, is placed in a cooler environment, its temperature will decrease at an exponential rate
until it reaches the temperature of the surroundings.
Entropy is a "state property," which is a quantity that depends only upon the current state of the system. Quantities
that are state properties do not depend on the path by which the system arrived at its present state. Therefore, the
most useful way to quantify a state property is to measure its change.
Now, let's see how to calculate the change in entropy, or ΔS. When talking about entropy, we must first define
the system. In this experiment, the system is the water, the surroundings are the air in the room. So the change in
entropy of the universe, or ΔS universe
is a sum of the change in entropies of these individual components, assuming
there is only energy exchange between water and air.
ΔS
universe
= ΔS
water
+ ΔS
air
Mathematically, the change in entropy is defined as heat gained or lost, denoted by q, divided by the temperature,
T, in Kelvin.
This equation can be applied to both the water and the air. When using this equation for water, then q is the heat
lost by water and T is the temperature of water in Kelvin. When using this equation for air, then q is the heat
gained by air and T is the temperature of air in Kelvin. We know that the hot water will cool spontaneously to the
surrounding temperature. Heat leaves water, or q has a negative sigh for water, thus ΔS water
is negative. Entropy
of water decreases. On the contrary, the surrounding air gains heat or q has a positive sign for air. Therefore, ΔS air
is positive. Entropy of the air increases. From the second law of the thermodynamics, we know that the change
in entropy of the universe must be positive for a spontaneous process. We will calculate the ΔS universe
at various
recorded temperatures.
Data table 1:
Air Temperature ________________
o
C, _______________________ Kelvins.
Volume of water used. ________________ mL
Mass of water used. Assuming density of water is 1.0 g/mL. ________________ grams
Time
Measured
Temp. of
Water
(
o
C)
Measured
Temp
Change of
Water
(
o
C)
q of
water
(J)
q of
air (J)
S
water
(J/K)
S
air
(J/K)
S
univ.
(J/K)
G
water
(kJ)
𝑙𝑛 (
𝑇(𝑡) − 𝑇
𝑠
𝑇
0
− 𝑇
𝑠
)
Calculated
Temp. of
Water (
o
C)
0’00’’
1’00’’
2’00’’
3’00’’
4’00’’
5’00’’
6’00’’
7’00’’
8’00’’
9’00’’
10’00’’
11’00’’
12’00’’
13’00’’
14’00’’
15’00’’
16’00’’
17’00’’
18’00’’
19’00’’
20’00’’
25’00’’
30’00’’
35’00’’
40’00’’
50’00’’
60’00’’
70’00’’
80’00’’
90’00’’
100’00’’
110’00’’
120’00’’
130’00’’
number of ways to distribute b identical objects into d distinguishable containers, using the combination
And in general, (
𝑛!
𝑘!
( 𝑛−𝑘
) !
, where factorial of n is n! = n ( n – 1)( n – 2) … 1. (1 point)
- The Haber process to produce ammonia involves the equilibrium
N 2 ( g ) + 3 H 2 ( g ) → 2 NH 3 ( g )
For this reaction, Δ H ° = – 92.38 kJ and Δ S ° = – 198.3 J/K. Assume that Δ H ° and Δ S ° for this reaction do
not change with temperature. (a) Predict the direction in which Δ G for the reaction changes with increasing
temperature. (b) Calculate Δ G at 25 °C and at 500 °C. ( 2 points)
Reference:
- JOVE.com/Science-Education
- Teaching and Learning Laboratory (TLL), and Singapore University of Technology and Design (SUTD) . RES.TLL- 004 STEM Concept Videos. Fall 2013. Massachusetts Institute of Technology: MIT
OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.
- https://math.berkeley.edu/~rhzhao/10BSpring19/Worksheets/Discussion%205%20Solutions.pdf
