Thermodynamics: Conceptual Question

In summary: So if you double it, the increase in entropy will also be large, but not necessarily by a factor of 2. In summary, when you double the number of possible microscopic states in a thermodynamic system, the entropy will increase, but by a factor greater than 2.
  • #1
cdlegendary
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1.Problem: A thermodynamic system has a large number of possible microscopic states. If you double the number of possible microscopic states, what happens to the entropy of the system?

it decreases
it remains the same
it increases, but by a factor less than 2
it increases by a factor greater than 2
it increases by a factor of 2
it increases, but not enough information is given to decide by what factor

2.Equations: S = k*ln(w), where s is entropy, k is the Boltzmann constant, and w is the # of microstates
3.Attempt: I did a couple tests with the equation, subbing in values of microstates. I developed an inconsistency, with it doubling by a factor of two with small numbers, and less than two with larger numbers. So I'm pretty sure the entropy increases, I just don't know by how much. Any help on explaining this to me would be appreciated.
 
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  • #2
cdlegendary said:
3.Attempt: I did a couple tests with the equation, subbing in values of microstates. I developed an inconsistency, with it doubling by a factor of two with small numbers, and less than two with larger numbers. So I'm pretty sure the entropy increases, I just don't know by how much. Any help on explaining this to me would be appreciated.
Why bother using small numbers for the microstates? The problem clearly states that the system has a large number of microstates.
 

1. What is thermodynamics?

Thermodynamics is the branch of science that deals with the study of energy and its transformation in physical systems. It involves understanding how energy is transferred between different forms and how it affects the behavior of matter.

2. What are the laws of thermodynamics?

The laws of thermodynamics are fundamental principles that govern energy transformation in physical systems. The first law states that energy cannot be created or destroyed, only transferred or converted. The second law states that the total entropy of a closed system will always increase over time. The third law states that the entropy of a perfect crystal at absolute zero temperature is zero.

3. What is the difference between heat and temperature in thermodynamics?

Heat and temperature are often used interchangeably, but they have different meanings in thermodynamics. Heat is the transfer of thermal energy from one object to another due to a temperature difference. Temperature, on the other hand, is a measure of the average kinetic energy of the particles in a system.

4. How does thermodynamics relate to everyday life?

Thermodynamics plays a crucial role in many everyday processes, such as cooking, refrigeration, and energy production. It helps us understand how these processes work and how we can make them more efficient. For example, understanding the second law of thermodynamics can help us design more efficient car engines and power plants.

5. What is the significance of thermodynamics in the study of climate change?

Thermodynamics is essential in understanding the Earth's climate and the effects of human activities on it. The laws of thermodynamics help us understand how energy is transferred in the atmosphere and how it affects the Earth's temperature. It is also used in climate models to predict future climate changes and inform policies to mitigate the effects of climate change.

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