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Problem 1: A spherical bulb is connected to a thin tube. The bulb and part of the tube are filled with ethanol. Assume that the bulb is a perfect sphere, and its inner radius is Rb=5mm, and the inner radius of the tube is Rt=0.5mm. The volume of the liquid ethanol inside the bulb will expand or shrink as temperature changes. The expansion is quantified by a thermal expansion coefficient defined in Eq 1 given below. For this homework, assume that the expansion coefficient is constant, =0.00125C1. a) Calculate the volume of the bulb. ( 2 points) b) When the surrounding temperature increases from 20 to 30C, a) Calculate the volumetric expansion of the ethanol inside the bulb. (5points) b) Calculate the liquid level change (increment h=h0h ) in the tube. Ignore the volume expansion inside the tube. (2 points) c) Plot V(T)/V0 vs T, using equations (4) or (4b) and (5) or (5b) given below. Compare the two curves. Select T=1,2,5,10,20,50,100C. (1 point) =V1dTdV(1)V(T)=V0exp[(TT0)](2)DefineT=TT0..(3)V0V(T)=exp(T)(4)Lety=V0V(T)y=exp(T)(4b)WhenT1V0V(T)=1+T(5)y=1+T.(5b)