Understanding the Problem:
We are given that when the pressure on a sphere is increased by 80 atm, its volume decreases by 0.01%. We need to find the bulk modulus of elasticity of the material of the sphere.

Key Formula:
The bulk modulus of elasticity (K) is defined as the ratio of the change in pressure (∆P) to the fractional change in volume (∆V/V) of a material. Mathematically, it can be expressed as:

K = -V (∆P/∆V)

Where:
K is the bulk modulus of elasticity
V is the initial volume of the sphere
∆P is the change in pressure
∆V is the change in volume

Solution:
Given:
Change in pressure (∆P) = 80 atm
Fractional change in volume (∆V/V) = 0.01% = 0.0001

To find the bulk modulus of elasticity (K), we need to determine the initial volume (V) and the change in volume (∆V).

Calculating the Change in Volume (∆V):
The fractional change in volume can be expressed as:

∆V/V = -V (∆P/∆V)

Rearranging the equation, we get:

∆V = -V (∆P/∆V) * V

Substituting the given values, we have:

∆V = -V (80 atm/0.0001)

Simplifying further:

∆V = -800,000 V atm

Calculating the Bulk Modulus of Elasticity (K):
We have the values of ∆P and ∆V, and we know that V is the initial volume of the sphere. Now, we can substitute these values into the formula for the bulk modulus of elasticity:

K = -V (∆P/∆V)

Substituting the values:

K = -V (80 atm/(-800,000 V atm))

Simplifying further:

K = 0.1 atm

Therefore, the bulk modulus of elasticity of the material of the sphere is 0.1 atm.

Conclusion:
The bulk modulus of elasticity of the material of the sphere is 0.1 atm. This indicates that the material is relatively compressible and can undergo significant changes in volume when subjected to pressure.

8×10^4 atm/m^3