Statistical Physics: very large and very small numbers

In summary, the conversation discusses the expression p = (1/44)^(10^5) and how it can be converted to 10^(-164345) analytically. The main difference between the two expressions is their base, and in order to compare them, they must have the same base. The solution is to convert (1/44) to a power of 10, and the rest follows easily. The conversation ends with gratitude for helping think through the problem.
  • #1
PhysicsGirl90
17
0
Working on statistical physics i came across this expression:

p = (1/44)^(10^5) = 10^(-164345)

However TI-83 calculator is unable to verify it (gives answer 0). Can someone tell me how to get from (1/44)^(10^5) to 10^(-164345) analytically?
 
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  • #2
You are still going to need to use a calculator at some point (their answer of 10^(-164345) is not exact, it has been rounded off). But yes, there is a way to find the answer which the calculator can cope with.

To start with, what is the main difference between the expressions (1/44)^(10^5) and 10^(-164345) ? Like if you wanted to compare the two numbers, what would be the first thing you would do?
 
  • #3
They have a different base. So if we wanted to compare them we they would both have to have the same base.
 
  • #4
exactly. So what can you do to get them both to have the same base?
 
  • #5
Thank you for your comment Bruce...i figured it out...convert (1/44) to a power of 10 and the rest follows easily.
 
  • #6
(1/44)^(10^5) = (10^log(1/44))^(10^5)...Thanks for helping me think it through.
 
  • #7
yeah, no worries. Glad to have helped :)
 

1. What is statistical physics?

Statistical physics is a branch of physics that studies systems with a large number of particles, such as atoms or molecules. It uses statistical methods to understand and predict the behavior of these systems.

2. What are very large numbers in statistical physics?

In statistical physics, very large numbers refer to the number of particles in a system. This can range from around 10^23 particles (Avogadro's number) to even larger numbers in certain systems.

3. What are very small numbers in statistical physics?

Very small numbers in statistical physics refer to values that are close to zero or very small compared to the total number of particles in a system. These values are important in understanding the behavior of individual particles within a larger system.

4. How are very large and very small numbers used in statistical physics?

Very large and very small numbers are used in statistical physics to describe and analyze the behavior of systems with a large number of particles. They are used in statistical calculations and equations to predict the macroscopic properties of a system based on the behavior of its individual particles.

5. What are some real-world applications of statistical physics?

Statistical physics has many real-world applications, including understanding the properties of matter, predicting the behavior of gases and liquids, and analyzing phase transitions. It is also used in fields such as materials science, cosmology, and biophysics.

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