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What pressure has to be applied to the e...

What pressure has to be applied to the ends of a steel cylinder to keep its length constant on raising its temperature by `100.^@C` ?

Text Solution

Verified by Experts

Variation of length with temperature is given by
`l_t=l_0(1+alphaDeltat)` or `(Deltal)/(l_0)=alphaDeltat=epsilon` (1)
But `epsilon=sigma/E`,
Thus `sigma=alphaDeltatE`, which is the sought stress of pressure.
Putting the value of `alpha` and `E` from Appendix and taking `Deltat=100^@C`, we get
`sigma=2*2xx10^3atm`.
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Knowledge Check

  • The pressure that has to be applied to the ends of a steel wire of length 10cm to keep its length constant when its temperature is raised by 100^@C is : (For steel Young's modulus is 2xx10^11 Nm^-2 and coefficient of thermal expansion is 1.1xx10^-5K^_1 )

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