Probability/entropy of spontaneous event

[so_gr_lo]

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

 

[haruspex]

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?

 

[jbriggs444]

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.

 

[haruspex]

Eventually

Unless that exceeds the lifetime of the universe.

 

[so_gr_lo]

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?

 

[haruspex]

The molecules have zero velocity at rest

Not if the pencil is at 15C.

 

[guv]

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.

 

[so_gr_lo]

These are the equations I have in my notes, are they the ones your referring to?