Calculate the increase in length of a 27cm brass rod that is heated from 10°C to 100°C. αbrass = 1.9 ×10–5 K–1.Question 15Answera.0.00049mb.0.0005mc.0.00043md.0.00046mClear my choiceCopyright © 2023 - Gibson School Systems. All Rights Reserved
Question
Calculate the increase in length of a 27cm brass rod that is heated from 10°C to 100°C. αbrass = 1.9 ×10–5 K–1.Question 15Answera.0.00049mb.0.0005mc.0.00043md.0.00046mClear my choiceCopyright © 2023 - Gibson School Systems. All Rights Reserved
Solution
The increase in length of a material due to heating can be calculated using the formula:
ΔL = L₀ * α * ΔT
where: ΔL is the change in length, L₀ is the initial length, α is the coefficient of linear expansion, and ΔT is the change in temperature.
Given: L₀ = 27 cm = 27 * 10^-2 m = 0.27 m (since 1 cm = 10^-2 m), α = 1.9 × 10–5 K–1, and ΔT = 100°C - 10°C = 90 K (since the Celsius and Kelvin scales are linearly related).
Substituting these values into the formula, we get:
ΔL = 0.27 m * 1.9 × 10–5 K–1 * 90 K = 0.000459 m = 4.59 × 10–4 m.
So, the increase in length of the brass rod is 4.59 × 10–4 m, which is closest to option a. 0.00049 m.
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