86degreeF. In a 24-hour period, the temperature can go from a day-time high of 9

Question

86degreeF. In a 24-hour period, the temperature can go from a day-time high of 93degreeF to a low of 31degreeF at night. By how many Celsius degrees does the temperature fall in the 24-hour period? By how many Kelvin degrees does the temperature fall in the 24-hour period? Suppose a meter stick made of steel and one made of invar are the same length at 0degreeC. What is their difference in length at 27.0degreeC? Repeat the calculation for two 35.0 m long surveyor's tapes. At a temperature of 24.20degreeC the hole in a steel plate has a diameter of 1.060 cm. If a steel rod with a diameter of 1.068 cm has to just slip through this hole, to what temperature should the plate be heated? The coefficient of area expansion of steel is 24 times 10^minus 6/degreeC.

Explanation / Answer

3) Invar 1.2 10^-6 /°C

Steel 13 10^-6 /°C

a) L = L° t
invar 1.2*10^-6 * 1 * 27 = 0.0324 mm
steel 13*10^-6 * 1 * 27 = 0.351 mm
difference in length at 27.0°C = 0.351 - 0.0324 = 0.3186 mm

b) invar 0.0324 *35 = 1.134 mm
steel 0.351 * 35 = 12.285 mm
difference in length at 27.0°C = 12.285 -1.134 = 11.151 mm

4) T1 = 24.2 C

A = (pi/4)*(1.06*10^-2)^2 = 8.82*10^-5 m^2

dA = (pi/4)*(0.008*10^-2)^2 = 5.03*10^-9 m^2

a = coefficient of area expansion = 24*10^-6 /oC

Now         a(T2 – T1) = dA/A

         24*10^-6*(T2 – 24.2) = 5.03*10^-9/8.82*10^-5

T2 = 26.58 C

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