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$$T=2$$×$$1011$$×$$11$$×$$10$$−$$6$$×$$100=2.2$$×$$103atm$$

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.

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