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in Heat and Thermodynamics by (48.5k points)
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A rod of metal -1 of length 50.0 cm elongates by 0.10 cm when it is heated from 0 °C to 100 °C. Another rod of metal-2 of length 80.0 cm elongates by 0.08 cm for the same rise in temperature. A third rod of length 50.0 cm, made by welding pieces of rod 1 rad and 2 rad placed end to end, elongates by 0.03 cm when it is heated from 0°C to 50°C.Then what is the length of metal1 in the third rod at 0°C?

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For metal-1,

\(a_1 = \frac{Δl}{lΔt} = \frac{0.10}{50.0 \times 100}\)

\(a_1 = 2.0 \times 10^{-5 }/ °C\)

For metal -2,

\(a_2\) = \(\frac{Δl}{lΔt}\) = \(\frac{0.08}{80.0 \times 100}\)

\(a_2\) = \(1.0 \times 10^{-5} / °C\)

Let the lengths of metal - 1 and metal - 2 in the third rod at 0°C be l1 and l2 respectively.

Then l1 + l2 = 50.0  ....(1)

When this rod is heated to 50°C, then

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