A steel scale measuresthe 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 40C ? (Given αsteel=11×10−6 per0 C and αcopper=17×10−6 per 0C)
80.0096 cm
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 temperature
Lapp=L′cu−L′steel=(L0(1+αcu△θ)−L0(1+αsteel△θ)
⇒Lapp=L0(αcu−αsteel)△θ
=80(17×10−6−11×10−6)×20=80.0096cm