Probability/entropy of spontaneous event

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In summary: Yes, those are the equations that you need to use to calculate the probability of the pencil spontaneously springing up in the air. The energy partition function and Boltzmann factor are used to relate the energy of a system to its temperature and the probability of a certain energy state occurring. In this case, you can use the energy partition function to calculate the probability of the pencil gaining enough energy from its surroundings to spring up in the air. From your result, you can conclude that the probability of this happening is very low, as it would require a significant amount of energy from the surroundings.
  • #1
so_gr_lo
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Homework Statement
What is the probability that a 10g pencil lying on a table will spring spontaneously 10cm into the air at the expense of thermal energy of its surroundings which are at 15°C. What do you conclude from your result?

I’m guessing I’m supposed to calculate the gravitational potential energy, which comes from the thermal energy of the surroundings, but I’m not sure how that relates to probability. In my course I’ve only been given entropy equations, not sure how it relates to probability
Relevant Equations
dS = dQ/T

U = mgh
I
FCAE2500-1A8C-47E6-81A7-39A96487CD82.jpeg
 
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  • #2
What is the difference in how the molecules of the pencil are moving between when it is lying at rest at 15C and when it is springing up in the air?
 
  • #3
so_gr_lo said:
Homework Statement:: What is the probability that a 10g pencil lying on a table will spring spontaneously 10cm into the air at the expense of thermal energy of its surroundings which are at 15°C. What do you conclude from your result?
Without calculating anything, the immediate answer is 100 percent. If it is permissible, it will happen. Eventually.

Probably the intent is to ask about leaving the system alone for a suitably long time and then inspecting it to see whether the pencil is or is not 10 cm in the air.
 
  • #4
jbriggs444 said:
Eventually
Unless that exceeds the lifetime of the universe.
 
  • #5
haruspex said:
What is the difference in how the molecules of the pencil are moving between when it is lying at rest at 15C and when it is springing up in the air?
The molecules have zero velocity at rest but a velocity in the air?
 
  • #6
so_gr_lo said:
The molecules have zero velocity at rest
Not if the pencil is at 15C.
 
  • #7
so_gr_lo said:
Homework Statement:: What is the probability that a 10g pencil lying on a table will spring spontaneously 10cm into the air at the expense of thermal energy of its surroundings which are at 15°C. What do you conclude from your result?

I’m guessing I’m supposed to calculate the gravitational potential energy, which comes from the thermal energy of the surroundings, but I’m not sure how that relates to probability. In my course I’ve only been given entropy equations, not sure how it relates to probability
Relevant Equations:: dS = dQ/T

U = mgh

IView attachment 300690
Entropy change is correct. For probability, you need to go back and look up your lecture note/book on energy partition function and Boltzmann factor.
 
  • #8
These are the equations I have in my notes, are they the ones your referring to?

5667E96D-C603-4872-95E6-EB80C003F49A.jpeg
 

FAQ: Probability/entropy of spontaneous event

What is the definition of probability in relation to spontaneous events?

Probability is a measure of the likelihood that a specific event will occur. In the context of spontaneous events, it refers to the chance that a particular event will happen without any external influence or intervention.

How is probability calculated for spontaneous events?

The calculation of probability for spontaneous events involves determining the number of possible outcomes and dividing it by the total number of possible outcomes. This gives a decimal value between 0 and 1, which can be interpreted as the probability of the event occurring.

What is entropy and how does it relate to spontaneous events?

Entropy is a measure of the randomness or disorder in a system. In the context of spontaneous events, it refers to the tendency of a system to move towards a state of higher disorder. This means that spontaneous events are more likely to occur in systems with higher entropy.

Can the probability of a spontaneous event be predicted?

No, the probability of a spontaneous event cannot be predicted with certainty. This is because spontaneous events occur without any external influence or intervention, making them inherently unpredictable. However, the probability of a spontaneous event can be estimated based on past occurrences and the current state of the system.

How can the probability of a spontaneous event be affected?

The probability of a spontaneous event can be affected by various factors, such as the initial conditions of a system, the presence of external influences, and the level of entropy in the system. Additionally, the probability of a spontaneous event can also be influenced by the laws of physics and chance events.

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