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)?
3 Answers
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
so
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