A circular...

**babygirl** · July 31st, 2006, 04:28 PM

A circular steel plate of radius 0.10 m is cooled from 350oC to 20oC. By what percentage does the plate's area decrease?

**CaptainBlack** · August 1st, 2006, 05:24 AM

Originally Posted by babygirl

A circular steel plate of radius 0.10 m is cooled from 350oC to 20oC. By what percentage does the plate's area decrease?

The coefficient of linear expansion of steel is $\alpha=12 \times 10^{-6}/^{\circ} K$ , so in coolling by $\Delta T=330^{\circ} C\ (=330^{\circ} K)$ the radius shrinks from $0.1\ \mbox{m}$ to $0.1-0.1\times \alpha \times \Delta T$ or by a fraction $\alpha \times \Delta T$ , so the area reduces by about twice this as a fraction or $2 \times \alpha \times \Delta T\approx 2 \times 12 \times 10^{-6} \times 330 = 0.00792$ , or $0.792 \%$ .

RonL

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