A steel scale measures the length of a copper wire as $$80.0$$ cm when both are at $$20$$°C (the$$ calibration temperature for $$scale). What would be the scale read for the length of the wire when both are at $$40$$°C? (Given$$ αsteel $$=$$ $$11$$×$$10-6$$ per °C and αcopper $$=$$ $$17$$×$$10-6per0C)

Question

A steel scale measures the length of a copper wire as $$80.0$$ cm when both are at $$20$$°C (the$$ calibration temperature for $$scale). What would be the scale read for the length of the wire when both are at $$40$$°C? (Given$$ αsteel $$=$$ $$11$$×$$10-6$$  per °C and αcopper $$=$$ $$17$$×$$10-6per0C)

Infinity Learn · Accepted Answer

With temperature rise (same$$ $$25$$°C for $$both), steel scale and copper wire both expand. Hence length of copper wire w.r.t. steel scale or apparent length of copper wire after rise in temperatureLapp $$=L0+$$ LCu'$$-Lsteel$$'        $$=L0+$$ [$$L0(1+$$αCu∆θ$$)-L0(1+$$αs∆θ$$)$$]⇒Lapp $$=L0+$$ $$L0($$α$$Cu-$$α$$s)$$∆θ              $$=80+$$ $$80(17$$×$$10-6-11$$×$$10-6)$$×$$20)$$               $$=$$ $$80.0096$$ cm

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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 scale). What would be the scale read for the length of the wire when both are at 40°C? (Given αsteel = 11×10-6 per °C and αcopper = 17×10-6per0C)

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