∆l=0.19
∆t=100′c
∆l=a∆t
a=∆l/∆t
a=0.19/100
we know that
y=3a
y=3*0.19/100
y=5.7*10^-5

Introduction:
The coefficient of volume expansion of a material describes how the volume of the material changes with temperature. It is denoted by the symbol β and is defined as the fractional change in volume per degree of temperature change.

Given:
- Length of the silver rod: 1 meter (100 cm)
- Initial temperature: 0 degrees Celsius
- Final temperature: 100 degrees Celsius
- Increase in length: 0.19 cm

Calculating the coefficient of volume expansion:
To calculate the coefficient of volume expansion of the silver rod, we can use the formula:

β = (ΔV / V₀) / ΔT

where:
- ΔV is the change in volume
- V₀ is the initial volume
- ΔT is the change in temperature

Calculating the change in volume:
Since we are given the change in length (ΔL), we can calculate the change in volume (ΔV) using the formula:

ΔV = A₀ * ΔL

where:
- A₀ is the initial cross-sectional area of the rod

Calculating the initial cross-sectional area:
The cross-sectional area of a rod is given by the formula:

A₀ = π * r₀²

where:
- r₀ is the initial radius of the rod

Calculating the change in temperature:
The change in temperature (ΔT) is given by:

ΔT = T - T₀

where:
- T is the final temperature
- T₀ is the initial temperature

Substituting the values into the formula:
Now, we can substitute the calculated values into the formula for the coefficient of volume expansion:

β = (ΔV / V₀) / ΔT

Conclusion:
By substituting the values calculated for ΔV, V₀, and ΔT into the formula for the coefficient of volume expansion, we can determine the value for β. This value represents the fractional change in volume per degree of temperature change for the silver rod.