A bimetal strip can be used as a thermometer and thermostat, a device that conve

Question

A bimetal strip can be used as a thermometer and thermostat, a device that converts small changes in temperature to mechanical motion (see figure A below). A thermostat can be constructed by joining two pieces of metal, brass and steel, along their length as shown in figure B below. The brass and steel are both 60 cm long and 0.12 mm thick. If this bimetal strip is heated, the brass will expand more than the steel, causing the strip to bend. What change in temperature is needed to make the bimetal strip curl to a full circle as shown in figure C below?

Explanation / Answer

Given

Lenth of one strip L = 0.60 m

Thickness of one strip t = 0.12 x 10-3 m

Known

Linear thermal expansionn coefficient of brass B = 19 x 10-6 K-1

Linear thermal expansionn coefficient of brass s = 13 x 10-6 K-1

Solution

The Difference in radius r1 - r2 = t = 0.12 x 10-3 m

The new length of the srips are equal to the circumference of the circles.

Circumference of brass circle SB = 2r1

Circumference of steel circle SS = 2r2

Change in length of the brass sripe

L = BLT

2r1 - L = BLT ….(1)

Change in length of the steel sripe

L = sLT

2r2- L = sLT   ….(2)

2r1 -2r2 = (B -s )LT

2(r1 -r2 ) = (B -s )LT

2t = (B -s )LT

T = 2t/(B -s )L

T = 2 x 3.14 x 0.12 x 10-3 / ( 19 x 10-6- 13 x 10-6) x 0.60

T = 209 OC

An increase in temperature by 209 oC would form a full circle

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