Question

A brass rod is two metre long at a certain temperature. What is the length for temperature rise of 100 kelvin if the expansivity of brass is 0.0000018/kelvin.

Answer 1

A brass rod is two metre long at a certain temperature. What is the length for temperature rise of 100 kelvin if the expansivity of brass is 0.0000018/kelvin.

Solution:

The change in length measurements of an object due to thermal expansion is related to temperature change by a linear expansion coefficient $(\alpha = 1.8 \times 10\mu \mathrm{K}^{-1})$. It is the fractional change in length per degree of temperature change. Assuming negligible effect of pressure, we may write:

$$\Delta \mathrm {L} = \mathrm {L} _ {0} \alpha \Delta \mathrm {T}, \quad \text {where} \mathrm {L} _ {0} = 2 \mathrm {m} - \text {initial length of the rod}$$ $$\mathrm {L} = \mathrm {L} _ {0} + \Delta \mathrm {L} = \mathrm {L} _ {0} (1 + \alpha \mathrm {T}) = 2 \mathrm {m} \cdot (1 + 1. 8 \times 1 0 \mu \mathrm {K} ^ {- 1} \cdot 1 0 0 \mathrm {K}) = 2. 0 0 0 3 6 \mathrm {m}$$

Answer: length of the brass rod for temperature rise of 100 kelvin is 2.00036m.

$$\Delta T = 1 0 0 K$$