You have been asked to make a thermometer, given a glass tube with some mercury

Question

You have been asked to make a thermometer, given a glass tube with some mercury inside. (There is nothing else in the tube, not even air.) At 0 C, the mercury just fills the bulb at one end of the thermometer, whose volume is 8mm^3. You make a mark at the top of the bulb indicating 0 C. At a higher temperature, the mercury rises through the tube. a) The coefficient of volume expansion of mercury is Beta=1.82X10^-4 (C)^-1. The hollow part of the thermometer, aside from the bulb at the end, is a cylinder with radius r=0.0250mm. Note that the volume of a cylinder with height h and r is (pi)r^2h. How far from the 0 degree mark should marks be made to indicate 1 C, 2 C, etc up to 100 C? You can ignore the thermal expansion of the glass tube. b) The coefficient of linear expansion of glass is alpha=9.00 X 10^-6 (C)^-1. iF the length of the thermometer of 0 C is 110mm, what is the length at 100 C. Was it appropriate to neglect the expansion of the glass? Explain why or why not. You have been asked to make a thermometer, given a glass tube with some mercury inside. (There is nothing else in the tube, not even air.) At 0 C, the mercury just fills the bulb at one end of the thermometer, whose volume is 8mm^3. You make a mark at the top of the bulb indicating 0 C. At a higher temperature, the mercury rises through the tube. a) The coefficient of volume expansion of mercury is Beta=1.82X10^-4 (C)^-1. The hollow part of the thermometer, aside from the bulb at the end, is a cylinder with radius r=0.0250mm. Note that the volume of a cylinder with height h and r is (pi)r^2h. How far from the 0 degree mark should marks be made to indicate 1 C, 2 C, etc up to 100 C? You can ignore the thermal expansion of the glass tube. b) The coefficient of linear expansion of glass is alpha=9.00 X 10^-6 (C)^-1. iF the length of the thermometer of 0 C is 110mm, what is the length at 100 C. Was it appropriate to neglect the expansion of the glass? Explain why or why not.

Explanation / Answer

Given initial volume of the thermometer V_1 = 8 mm^3 = 8*10^ -9 m^3 Coefficient of volume expansion   ß = 1.82*10^ -4   C^ -1 radius of the cylinder     r = 0.025 mm = 0.025*10^ -3 m Volume of the cylinder   V_2 =   p r^2   h                                            = 3.14 * ( 0.025^2 * 10^ -6 ) h   a)                       Volume expansion                     ? V = V_1 (ß ?T)           change in temperature   ?T = ( V_2 - V_1 ) / V_1 ß b) initial length L = 110 mm = 0.1 m      coefficient of linear expansion   a = 9*10^ -6           ?T = 100 linear expansion                    L = L_o ( 1 + a ?T )                       = 0.1 ( 1 + 9*10^ -6 * 10^ 2 )                       = 0.1 ( 1 + 9*10^ -4 )                         = 0.10009 m

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