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 59 cm long and 0.14 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 into a full circle as shown in figure C below? Hint: The difference in the radius of the two metals making the strip is just the thickness of one metal strip.

_______________K?

Explanation / Answer

let

Lo = 59 cm

t = 0.14 mm

= 0.014 cm

we know,

alfa_brass = 18.7*10^-6 K^-1

alfa_steel = 12.0*10^-6 K^-1

when the temperature is incresed,

L_brass = Lo + Lo*alfa_brass*dT

L_steel = Lo + Lo*alfa_stell*dT

L_brass - L_steel = Lo*(alfa_brass - alfa_steel)*dT

2*pi*r2 - 2*pi*r1 = Lo*(alfa_brass - alfa_steel)*dT

2*pi*(r2-r1) = Lo*(alfa_brass - alfa_steel)*dT

2*pi*t = Lo*(alfa_brass - alfa_steel)*dT

==> dT = 2*pi*t/(Lo*(alfa_brass - alfa_steel))

= 2*pi*0.014/(59*(18.7 - 12)*10^-6)

= 223 K <<<<<<<<----------------------Answer

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