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# An Analysis of Black Hole Thermodynamics

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Contents

## Introduction

Today we will do an analysis of black hole thermodynamics. This science experiment will help us determine the effect of the universe’s temperature on the Black Hole as the universe ages.

## Aim

To determine how the black hole gets affected by the universe’s temperature.

## Theory

1. The Schwarzchild radius equation of any object of mass M is given by,

rs = 2GM/c^(2)

‘G’ is the gravitational constant,

‘M’ is the mass of the object, and

‘c’ is the speed of light.

kT=ℏg2πc=ℏc4πrs

‘T’ is temperature, ‘ℏ’ = h/(2π),

where ‘h’ is Planck’s constant,

‘g’ is the surface gravity, and

‘k’ is Boltzmann’s constant.

A Black Hole

2. Notebook

3. Pen

## Procedure

Step 1: With the help of the classic Schwarzschild Radius formula, determine the size of the black hole.

Step 2: With the help of Stephen Hawking’s Radiation, determine the amount of energy being radiated through the black hole.

Step 3: Now, measure the temperature of the black hole.

Step 4: Compare the temperature of the universe with the temperature of the black hole.

Step 5: Now, find out how long the temperature of the universe will take to reach equilibrium with the temperature of the black hole.

Step 6: Set up all these equations in an excel spreadsheet.

Step 7: Solve 1 to 512 solar masses for black holes.

Step 8: Also explore the results of smaller black holes, the moon, the mass of earth, and savy-suburban, for instance.

## Observation

1. We observed that the larger the black hole, the longer it will take for the temperature of the universe to reach equilibrium with the temperature of the black hole.

2. After reaching equilibrium, a larger black hole will radiate less than the smaller one. Therefore, a larger black hole will take longer to radiate all of its mass away.

## Result

1. Our hypothesis is correct. When the universe expanded and cooled, it was absorbing less CMB than it was radiating; in this way, it lost mass and eventually radiated all the mass and evaporated.

2. Large solar masses would take longer to reach equilibrium with the temperature of the universe and take even longer to radiate all their masses away.

## Precautions

1. Put the values correctly in all equations.

## Conclusion

We performed an analysis of black hole thermodynamics, and we have determined the black hole thermodynamics in which I experimented with the effect of the temperature of the universe on the black hole.

Q.1 What was the aim of your experiment?

ANS. To determine how the black hole gets affected by the temperature of the universe.

Q.2 What is the effect size of the lack of holes on the temperature of the universe?

ANS. The larger the black hole, the longer it will take for the temperature of the universe to reach equilibrium with the temperature of a black hole.

Q.3 What kind of solar mass would take longer to reach equilibrium?

ANS. Large solar masses would take longer to reach equilibrium with the temperature of the universe.

Q.4 What is the equation of Stephen Hawking’s radiation?

ANS. kT=ℏg2πc=ℏc4πrs

Where ‘T’ is temperature, ‘ℏ’ = h/(2π), where ‘h’ is Planck’s constant, ‘g’ is the surface gravity, and ‘k’ is Boltzmann’s constant.

Q.5 Which type of black hole takes a longer time to radiate all its masses away?

ANS. The large black hole will take a longer time to radiate all of its mass away.

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