Help! You want to make a fast response thermometer. In order to do so, you decid

Question

Help!

You want to make a fast response thermometer. In order to do so, you decide to use an aluminum bulb to hold the liquid which will rise through a glass tube at the top, like normal thermometers. For AI, a= 22.2x10-6 /K The liquid used is ethylene glycol which has a volume expansion coefficient= 0.00057 /K and the glass can be treated as not expanding over the temperatures of interest. The bulb is spherical and has a volume of 1 cm3 at 20 degree C. The liquid fills the bulb and the first 4cm of the tubing whose inner diameter is 0.05 cm. When the bulb is warmed to 50 degree C, what is the new volume of the bulb? What is the volume of the liquid? How high in the glass tubing will the liquid be? repeat the calculations in part (a) for 100 degree C.

Explanation / Answer

a)volume of bulb at 50 degrees=1+3*22.2*10^(-6)*30*1=1.002cc

initial vol. of liquid=1.0314cc

on expansion vol. of liquid=1.0314+0.00057*30*1.0314=1.05cc

vol. of liquid out of bulb=1.05-1.002=0.048cc

thus height=0.048/(3.14*0.05*0.05)=6.115cm

b)volume of bulb at 100 degrees=1+3*22.2*10^(-6)*80*1=1.005cc

initial vol. of liquid=1.0314cc

on expansion vol. of liquid=1.0314+0.00057*80*1.0314=1.08cc

vol. of liquid out of bulb=1.08-1.005=0.075cc

thus height=0.075/(3.14*0.05*0.05)=9.554cm

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