Question

11. 2. A steel scale measures the length of a copper rod as 80 cm when both are at 20°C, the calibration temperature of the scale. What would the scale read for the length of the rod when both are at 40°C? Given a for steel = 1.1 x 10-5°C-1 and a for copper 1.7 x 10-5 °C-1. ​

Answer 1

Given

• Steel scale measures the length of a copper rod as 80 cm at 20°C
• α(s) = 1.1 × 10⁻⁵
• α(c) = 1.7 × 10⁻⁵

To Find

• Length of the copper rod at 40°C

Solution

☯ L = L₀(1+α∆T)

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✭ According to the Question :

We know that,

• L(c) = L₀(1+α꜀∆T)
• L(c) = L₀(1+α꜀∆T)L(s) = L₀(1+αₛ∆T)

⇒ L(final) = L(c) - L(s)

⇒ L(final) = [ L₀(1+α꜀∆T) - L₀(1+αₛ∆T) ]

⇒ L(final) = L₀(1 + {α꜀ - αₛ} ∆T)

⇒ L(final) = L₀(1 + {1.7 × 10⁻⁵ - 1.1 × 10⁻⁵ } × {40-20})

⇒ L(final) = L₀(1 + {0.6 × 10⁻⁵} × 20)

⇒ L(final) = L₀(1+0.00012)

⇒ L(final) = L₀(1.00012)

⇒ L(final) = 80(1.00012)

⇒ L(final) = 80.0096 cm

∴ The length of the copper rod at 40°C will be 80.0096 cm

Answer 2

Answer:

A steel scale measures the length of a copper rod as 80 cm when both are at 20°C, the calibration temperature of the scale. What would the scale read for the length of the rod when both are at 40°C ? Given a for steel = 1.1 x 10-5°C-1 and a for copper = 1.7 x 10-5°C-1 (Ans. 80.0096 cm)