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A steel beam used in the construction of a bridge has a length of 30.0 m when the temperature is 15^(@)C. On a very hot day, when the temperature is 35^(@)C, what will the beam's change in length be? (The coefficient of linear expansion for structural steel is +1.2xx10^(-5)//""^(@)C.) |
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Answer» Solution :The change in LENGTH o the beam is `DeltaL=alphaL_(0)DeltaT=(1.2xx10^(-5))/(""^(@)C)(30.0m)(35^(@)C-15^(@)C)=7.2xx10^(-3)m=7.2mm` As we're mentioned, substances also undergo volume changes when HEAT is lost or ABSORBED. The change in volume `DeltaV`, corresponding to a temperature change, `DeltaT`, is GIVEN by the equation `DeltaV=betaV_(0)DeltaT` Where `V_(0)` is the sample's initialvolume and `beta` is the coefficient of volume expansion of the substance. since we're now LOOKING at the change in a three-dimensional quantity (volume) rather than a one-dimensional quantity (length), for most solids, `beta=3alpha`. nearly all substances have a positive value of `beta`, which means they expand upon heating, an extremely important example of a substance with a negative value of `beta` is liquid water between `0^(@)C and 4^(@)C`. unlike the vast majority of substances, liquid water expands as it nears its freezing point and solidifies (which is why ice has a lower density and floats in water). |
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