Entropy and damping osscilations

In summary, for question 1, in order to calculate the change in entropy for a constant pressure process, you need to integrate dS from the initial to the final temperature. To relate dQ to dT, you can use the heat capacity for constant pressure processes.For question 2, you can set up an equation using the given information and the fact that the amplitude decreases by 3/4 after 4 cycles. This will allow you to solve for the period, which you can then use to calculate the spring constant using the equation F=-bv. Using w^2=k/m may not be correct in this case since it is a damped oscillator.
  • #1
ilovephysics
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i just have 2 questions i want to clear up so i can understand the concepts more, thanks

1) if you are calculation entropy change from path a to b and the path is isobaric (cont. pressure) how do you do it? the formula for entropy change is dQ/T, but i am unsure about what T to use, also i cannot use mclnT2/T1 because i do not know the mass of the gas, how should i solve a problem like this?

2) if you are given the mass of an object and spring const., initial amplitude and info that the amplitude is 3/4 of what it was initially in 4 cycles, how do you calculate b, we don't know the period but do we use w^2=k/m? the question, being about damped ossilators throws me off a bit and I am unsure how to start a problem like this
 
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  • #2
Regarding question 1, I assume we are talking ideal gas here? In order to calculate the change in entropy you need to integrate dS from the initial to the final temperature. Can you find a way to relate dQ to dT? Hint: think about the heat capacity for constant pressure processes.

Regarding question 2, you know how long it takes to execute each cycle, right? Try setting up an equation that tells you that [tex] x(4T) = \frac{3}{4} x(0) [/tex]. Where [tex] T [/tex] is the "period" of the system (though the system isn't actually periodic, this is simply the period of the periodic part).
 
  • #3
yes it is a monoatomic ideal gas, when we integrade dS we get mCvln(t2/t1) don't we? i am unsure where to go from there because we do not know the mass

for question 2, we are not given the time it takes to complete each cycle, we are given mass, spring const, initial A, A after 4 cycles, and the equation F=-bv, when i did this question i just used w^2=k/m and found the period that way but I am pretty sure that isn't correct since its about a damped osscilator
 

1. What is entropy and how does it relate to damping oscillations?

Entropy is a measure of the disorder or randomness in a system. In the context of damping oscillations, entropy is related to the amount of energy that is dissipated or lost due to damping. As the system oscillates, the energy is continually being converted from potential energy to kinetic energy and back again. Damping reduces the amount of energy available for oscillation, leading to a decrease in entropy.

2. How does damping affect the amplitude and frequency of oscillations?

Damping has a direct effect on both the amplitude and frequency of oscillations. As damping increases, the amplitude of the oscillations decreases. This is because the energy is being dissipated, leading to smaller and smaller oscillations. Additionally, damping also affects the frequency of oscillations. In most cases, the higher the damping, the lower the frequency of the oscillations.

3. Can entropy be reversed in a damping oscillation system?

No, entropy is a fundamental law of thermodynamics and cannot be reversed in a damping oscillation system. As energy is lost due to damping, the system becomes more disordered, leading to an increase in entropy. This process is irreversible and the system will continue to lose energy and increase entropy until it reaches a state of equilibrium.

4. Is there a relationship between damping and the quality factor (Q) of a system?

Yes, there is a relationship between damping and the quality factor (Q) of a system. The quality factor is a measure of how long the system can sustain an oscillation before the energy is completely dissipated. A higher quality factor indicates a lower amount of damping, meaning the system can sustain oscillations for a longer period of time.

5. How do different types of damping affect oscillation behavior?

Different types of damping, such as viscous, Coulomb, and hysteretic damping, all have different effects on oscillation behavior. Viscous damping, for example, is proportional to velocity and leads to a decrease in amplitude and frequency of oscillations. Coulomb damping, on the other hand, is independent of velocity and can lead to chaotic oscillations. Hysteretic damping is caused by internal friction and can result in a decrease in amplitude over time.

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