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Chapter 3: Q19E (page 575)

A machinist bores a hole of diameter 1.35 cm in a steel plate that is at 25.0潞C. What is the cross-sectional area of the hole (a) at 25.0潞C and (b) when the temperature of the plate is increased to 175潞C? Assume that the coefficient of linear expansion remains constant over this temperature range.

Short Answer

Expert verified

(a) The cross sectional area of the hole at 25.0潞C is 1.431鈥�cm2.

(b) The cross sectional area of the hole at increased temperature of 175.0潞C is 1.436鈥�cm2.

Step by step solution

01

Concept of Area Expansion in solids.

Area expansion is the expansion of the dimensions of an object with respect to temperature changes and can be expressed as,

螖础=2伪础0螖罢 ...(i)

Here, A is the expansion in area, A0 is the unexpanded area, 伪 is the coefficient of volume expansion and T is the absolute temperature.

02

 Determination of the diameter value of the rivet following the conditions mentioned.

For steel, the coefficient of area expansion,

伪=1.2脳10-5鈥�(C慰)(-1)

The unchanged original area is,

A0=蟺谤02=蟺1.350cm22=1.431cm2

Calculate the area change for the steel using equation (i),

螖础=2伪础0螖罢

Substitute all the values in the above equation,

鈭�As=21.2脳10-5C0-11.431cm2175C0-25C0=5.15脳10-3cm2

Thus, cross sectional area at 175.0潞C

A=A0+鈭�A=1.436cm2

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