Thermal Properties of Matter

JEE Main level, single correct, medium

45 of 126

Question 45 of 126

The pressure that has to be applied to the ends of a steel wire of length 10cm10cm to keep its length constant when its temperature is raised by 100∘C100^{\circ}C is :
(For steel, Young's modulus is
2×1011Nm−22\times {10}^{11}N{m}^{-2} and coefficient of thermal expansion is 1.1×10−5K−11.1\times {10}^{-5}{K}^{-1})

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Answer: (A) 2.2×108Pa2.2\times {10}^{8}Pa

Young's modulus, Y=FALΔLY=\dfrac{F}{A}\dfrac{L}{\Delta L}

∴FA=YΔLL=YαΔT∴ \dfrac{F}{A}=Y\dfrac{\Delta L}{L}=Y\alpha \Delta T

∴P=2×​1011×1.1×10−5×102∴ P=2{\times ​ 10}^{11}\times 1.1\times {10}^{-5}\times {10}^{2}

∴P=2.2×108Pa∴P=2.2\times {10}^{8}Pa

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