please show work and explain A 16.0-m-long bar of steel expands due to a tempera

Question

please show work and explain

A 16.0-m-long bar of steel expands due to a temperature i A 8.0-m-long bar of copper also gets longer due to the same temperature rise. If the two bars were originally separated by a gap of d 1.1 cm, calculate the change in temperature and the distances that the steel and copper stretch if the gap is exactly "closed" by the expanding bars. Assume the steel and copper bars are fixed on the ends, as shown in the figure below. AT AL mm stee mm Cu Initial: Copper bar Steel bar Final:

Explanation / Answer

coefficient of thermal expansion of copper = 17e-6

coefficient of thermal expansion of steel= 13e-6

Now we have,

0.011 m = 13e-6 *16m*T + 17e-6 *8m *T

T = 0.011m/[13e-6 *16m*+ 17e-6 *8m ]

T =31.98 K

delta Lsteel = 31.98* 13e-6 *16m = 6.65 mm

delta Lcopper = 31.98* 17e-6 *8m =4.35 mm

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