Entropy and Thermal Equilibrium: Solving the Hotter-Colder Object Conundrum

In summary, the Boltzmann equation states that the entropy of a system is proportional to the logarithm of the number of particles in the system.
  • #1
zeithief
29
0
I stumbled across this question in one of the physics competition selection test but after thinking like 2 days i still can't figure out homework to solve it.
I've been introduced to the equation: entropy, S=Q/T where Q is the heat energy and T is the temperature.
Then I've been told that the entropy of a system always remains constant or increase.
Then the question is to show that when a hotter object and a colder object are put together and isolated the hotter object always becomes colder and colder becomes hotter. We are expected to solve this with the information provided only.
Help anyone ?? :biggrin: ?
 
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  • #2
  • #3
zeithief said:
I stumbled across this question in one of the physics competition selection test but after thinking like 2 days i still can't figure out homework to solve it.
I've been introduced to the equation: entropy, S=Q/T where Q is the heat energy and T is the temperature.
Then I've been told that the entropy of a system always remains constant or increase.
Then the question is to show that when a hotter object and a colder object are put together and isolated the hotter object always becomes colder and colder becomes hotter. We are expected to solve this with the information provided only.
As Cyrus says, you must look at the change in entropy, which according to the second law of Thermodynamics, must be greater than or equal to zero. Assume the flow of heat is from the colder to the hotter object and determine whether the change in entropy of the system is greater than zero. See if it fits with the second law.

The change entropy of the system is the sum of the entropy changes in each object. Use the convention: heat flow into an object is positive and heat flow out is negative. dS = dQ/T

AM
 
  • #4
zeithief said:
Then the question is to show that when a hotter object and a colder object are put together and isolated the hotter object always becomes colder and colder becomes hotter. We are expected to solve this with the information provided only.
Help anyone ?? :biggrin: ?

We already know the equation delta S = delta Q(reversible) / T

Now we want to explain the way in which spontaneous processes occur using the entropy. Assume two spaces, one space has temperature T1 and the other T2 and we isolate this system.

The difference between the two entropies delta S at equilibrium is given by:

delta S = delta S(1) + delta S(2)

(total entropy change of the system is the sum of the two separate entropy changes)

Now we can write: delta S(1) = delta Q(reversible)(1) / T(1) and delta S(2) = delta Q(reversible)(2) / T2. Now because the system is isolated, Q(rev)1 = -Q(rev)2 (heat released by 1 must be taken up by 2). We say Q = Q(rev)1 = -Q(rev)2

delta S = Q(1/T1 - 1/T2)

Now we say that when T2 > T1 then delta S > 0 (spontaneous process) when Q > 0, so heat flows into system 1 . When T1 > T2, delta S > 0 when Q < 0 and thus heat flows into system 2.
 
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  • #5
we see microsopic and macroscopic entropy differnetly ..
microscopic is about statistical view of entropy?
what can we say about the boltz man equation of entropy
 
  • #6
ashu_manoo12 said:
we see microsopic and macroscopic entropy differnetly ..
microscopic is about statistical view of entropy?
what can we say about the boltz man equation of entropy

you mean S = k * ln W :p
 

1. What is entropy?

Entropy is a measure of the disorder or randomness in a system. It is a fundamental concept in thermodynamics and is often referred to as the "arrow of time" because it describes the tendency of systems to become more disordered over time.

2. How is entropy related to thermal equilibrium?

Thermal equilibrium is a state in which two or more objects or systems have the same temperature. In this state, there is no net flow of heat between them. Entropy is closely related to thermal equilibrium because in a closed system, the total entropy will tend to increase until thermal equilibrium is reached.

3. Can entropy be reversed?

No, according to the second law of thermodynamics, the total entropy of a closed system will always increase over time. This means that once a system has reached a state of maximum entropy, it cannot be reversed.

4. How does entropy affect energy transfer?

Entropy plays a crucial role in energy transfer. In order for energy to be transferred from one system to another, there must be a difference in entropy between the two systems. This difference in entropy is what drives the transfer of energy.

5. How do scientists measure entropy?

Entropy is typically measured using statistical mechanics, which uses mathematical models to describe the behavior of large numbers of particles. Scientists can also measure the change in entropy of a system by measuring the change in its temperature and energy over time.

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