To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.860cm in diameter is to be placed in a hole 1.856cm in diameter. To what temperature (on the Celsius scale) must the rivet be cooled if it is to fit in the hole (at 20.0oC)?
Assume linear thermal coefficient of expansion of steel is 1.3 x 10^-5 /degree C (should be given in question, can vary between 1.0 and 1.8 x 10^-5 /C depending on steel composition)
We need to shrink the rivet by 0.004 cm in 1.860 cm or by 0.004/1.860 = 0.002150538 cm/cm
each degree will shrink by 0.000013 cm/cm
0.002150538 / 0.000013 = 165.426
we need to cool the rivet by 165.426 degrees i.e. to -145.426 degrees C.
This is not usual,. The process of riveting usually causes enough expansion of the stem of the rivet when forming the counter head to ensure a tight fit. It is often easier to heat the work-piece rather than cool the rivet. Steel rivets are often inserted red-hot to enable forming of the head.
you could desire to be conscious this equation. deltaA/Ainitial=2x@xdeltaT A=part in meters @=coeficient of thermal enlargement for metallic (looks like a million/2 of an infinity image) it is 12×10^-6 T=temperature in degrees C or ok(the two will artwork) resolve the equation for deltaT and plug in numbers. after you have the deltaT subtract it from 20 degrees C because of the actuality it is going to be chillier.
you have to use 12*10^-6 cm/cm to find delta T for lon capa program