Thermal expansion

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Question

The magnitude of force developed by raising the temperature from $0^{o} C to 100^{o} C$ of an iron bar 1m long and of $1 {cm}^{2}$ cross section when it is held between two rigid walls so that it is not permitted to expand is $(α = 10^{- 5} /^{o} C and Y = 10^{11} N / m^{2})$

Moderate

Solution

Induced compressive force =Thermal stress X cross section
$∴ F = (Yα . Δθ) S = 10^{11} \times 10^{- 5} \times 100 \times 10^{- 4} N = 10^{4} N$

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