Coefficient of Volume Expansion of Silver at Different Temperatures

In this article, we will explore the coefficient of volume expansion of silver, specifically focusing on how a silver rod changes in volume when heated from 0°C to 100°C and 0°C to 200°C.

Introduction to Coefficients of Expansion

When materials are subjected to changes in temperature, they tend to expand or contract. This is quantified by two coefficients: linear expansion and volume expansion. The linear expansion coefficient, α, describes the change in length, while the volume expansion coefficient, β, describes the change in volume.

Deriving the Coefficient of Volume Expansion

The relationship between the coefficient of linear expansion α and the coefficient of volume expansion β is given by:

β 3α

Example Calculation for 0°C to 100°C

Consider a silver rod of 1 meter in length at 0°C. When heated to 100°C, its length increases by 0.19 cm. We will use this information to calculate the coefficient of volume expansion of silver.

Step 1: Determining the Coefficient of Linear Expansion

The formula for linear expansion is:

ΔL L?αΔT

Where:

ΔL change in length L? original length α coefficient of linear expansion ΔT change in temperature

Given:

ΔL 0.19 cm 0.0019 m L? 1 m ΔT 100°C - 0°C 100°C

Plugging in the values:

0.0019 1 · α · 100

α 0.0019 / 100 1.9 × 10-5 per °C

Step 2: Calculating the Coefficient of Volume Expansion

Using the relationship between the coefficients:

β 3α

β 3 × 1.9 × 10-5 5.7 × 10-5 per °C

Example Calculation for 0°C to 200°C

Now, consider the same silver rod heated to 200°C from 0°C. The length increases by 0.19 cm. Using similar steps:

Step 1: Determining the Coefficient of Linear Expansion

Given:

ΔL 0.19 cm 0.0019 m L? 1 m ΔT 200°C - 0°C 200°C

Plugging in the values:

0.0019 1 · α · 200

α 0.0019 / 200 9.5 × 10-6 per °C

Step 2: Calculating the Coefficient of Volume Expansion

Using the relationship between the coefficients:

β 3α

β 3 × 9.5 × 10-6 2.85 × 10-5 per °C

Conclusion

The calculated coefficient of volume expansion for the first scenario (0°C to 100°C) is approximately:

β ≈ 5.7 × 10-5 per °C

And for the second scenario (0°C to 200°C) is approximately:

β ≈ 2.85 × 10-5 per °C

This difference in coefficients is due to the higher temperature range in the second scenario, which can be observed from the reduced coefficient of linear expansion.

References

This article is based on the principles of thermal expansion and material properties as described by [Link to source].