The length of a steel cylinder is kept constant by applying pressure at its two ends. When the temperature of rod is increased by $$100oC$$ from its initial temperature, the increase in pressure to be applied at its ends is Ysteel $$=2$$×$$1011N/m2$$,αsteel $$=11$$×$$10$$−$$6/$$∘C,$$1atm=105N/m2$$.

Question

The length of a steel cylinder is kept constant by applying pressure at its two ends. When the temperature of rod is increased by $$100oC$$ from its initial temperature, the increase in pressure to be applied at its ends is Ysteel $$=2$$×$$1011N/m2$$,αsteel $$=11$$×$$10$$−$$6/$$∘C,$$1atm=105N/m2$$.

Infinity Learn · Accepted Answer

If the rod is allowed to expand, then it will expand by Δ$$l=l$$α ΔT due to increase in temperature by ΔT. But as the length of the cylinder is kept constant by applying pressure, a stress is developed in the cylinder. The decrease in length of cylinder due to elasticity is Δ$$l=l$$αΔT and a compressive stress will develop in it.Stress $$=$$ Excess pressure applied at ends∆$$P=Y$$×Δ$$ll=Y$$αΔ$$T=2$$×$$1011$$×$$11$$×$$10$$−$$6$$×$$100=2.2$$×$$103atm$$

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