A steel scale measures the length of a copper wire as $$80.0$$ cm, when both are at $$20$$°C, the calibration temperature for the scale. What would the scale read for the length of the wire when both are at $$40$$°C ? (Given$$ : α for steel $$=11$$ $$x10-6$$ per °C and α for Cu $$=$$ $$17$$ x $$10-6$$ per °$$C)

Question

A steel scale measures the length of a copper wire as $$80.0$$ cm, when both are at $$20$$°C, the calibration temperature for the scale. What would the scale read for the length of the wire when both are at $$40$$°C ? (Given$$ : α for steel $$=11$$ $$x10-6$$ per °C and α for Cu $$=$$ $$17$$ x $$10-6$$ per °$$C)

Infinity Learn · Accepted Answer

We know $$that4=l0(1+$$α$$t)=11+11$$×$$10$$−$$6$$×$$40$$∘−$$20$$∘$$=1$$⋅$$00022cmNow$$ the length of copper rod at $$40$$°$$Cl1$$′$$=l0$$′$$1+$$α′$$t=801+17$$×$$10$$−$$6$$×$$(40$$−$$20)=80$$⋅$$0272cmNumber$$ of cms observed on the $$scale=80$$⋅$$02721$$⋅$$00022=80$$⋅$$0096$$

A steel scale measures the length of a copper wire as 80.0 cm, when both are at 20°C, the calibration temperature for the scale. What would the scale read for the length of the wire when both are at 40°C ? (Given : $α$ for steel =11 x10^-6 per °C and $α$ for Cu = 17 x 10^-6 per °C)

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A steel scale measures the length of a copper wire as 80.0 cm, when both are at 20°C, the calibration temperature for the scale. What would the scale read for the length of the wire when both are at 40°C ? (Given : α for steel =11 x10-6 per °C and α for Cu = 17 x 10-6 per °C)

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Ready to Test Your Skills?

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A steel scale measures the length of a copper wire as 80.0 cm, when both are at 20°C, the calibration temperature for the scale. What would the scale read for the length of the wire when both are at 40°C ? (Given : $α$ for steel =11 x10^-6 per °C and $α$ for Cu = 17 x 10^-6 per °C)