A casserole dish has coefficient of linear expansion 7.5 times 10^-6 (C degree)^

Question

A casserole dish has coefficient of linear expansion 7.5 times 10^-6 (C degree)^-1. When the casserole dish is removed from ice water and place in an oven at 175 degree C, it expands 0.0250 cm. How long was the casserole dish before being placed in the oven? Write your result with two significant figures. A steel rod with length 2.65 m at -5.00 degree C is heated to 50.00 degree C. How much does the rod expand? Give your answer in centimeters with two significant figures. The coefficient of linear expansion for steel is 12 times 10^-6 (C degree)^-1.

Explanation / Answer

(1)
the coefficient of linear expansion is given by the formula

alpha = change in length / (original length * change in temp)

so

alpha = change in diameter /( original diameter * change in temp)

Given alpha = 7.5 * 10-6 /C

change in length = 0.025 cm

change in temp = 175 - 0= 175 C

So alpha = 0.025 / ( L * 175 )

7.5 * 10-6 =0.025 / 175 L

175 L = 0.025 / 7.5 * 10-6

L = 19.0476 cm

So original length of dish is 19.0476 cm

(2)
The coefficient of linear expansion is given by the formula

alpha = change in length / (original length * change in temp)

Given alpha = 12 * 10-6 /C

original length = 2.65 m

change in temp = final - initial

= 50 - (-5)

= 50 +5

= 55 C

So

alpha = change in length / ( 2.65 * 55)

12 * 10-6 = change in length / 145.75

change in length =1749 * 10-6 m

=1749 * 10-3 mm

So the change in length is 1749 * 10-3 millimeters

The rod expands by 1749 * 10-3 millimeters

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