The length L (in centimeters) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L interms of C.

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Solution

$Assuming C along x-axis and L along the y-axis, we have two points, (20, 124.942) and (110, 125.134), in CL-plane. As L is a linear function of C, the equation of the line passing through (20, 124.942) and (110, 125.134) is L - 124.942 = \frac{125.134 - 124.942}{110 - 20} (C - 20) \Rightarrow L - 124.942 = \frac{0.192}{90} (C - 20) \Rightarrow L - 124.942 = \frac{0.032}{15} (C - 20) \Rightarrow L = \frac{0.032}{15} C + 124.942 - \frac{20 \times 0.032}{15} \Rightarrow L = \frac{0.032}{15} C + 124.942 - 0.04267 \Rightarrow L = \frac{4}{1875} C + 124.899$

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Q. The length L (in centimeters) of a copper rod is a linear function of its celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.

The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.

A steel scale measures the length of a copper rod as L cm when both are at $20^{\circ} C$ , the calibration temperature for the scale. If the coefficients of linear expansion for steel and copper are $α_{s}$ and $α_{c}$ respectively, what would be the scale reading (in cm) when both are at $21^{\circ} C$ ?

Q. A steel scale measures the length of a copper rod as

L cm

when both are at

20^{\circ} C

, the calibration temperature for the scale. If the coefficients of linear expansion for steel and copper are

α_{s}

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