When the bar is heated but not allowed to expand, thermal stress develops. The stress σ is given by σ = YαΔT, where Y is Young's modulus, α is the coefficient of linear expansion, and ΔT is the temperature change.

The elastic energy per unit volume U is (1/2) × (stress × strain). Since strain = σ/Y, this simplifies to U = (1/2) × (σ²/Y).

Substituting for σ gives U = (1/2) × Y × (αΔT)².

Total energy E = U × Volume = (1/2) × Y × (αΔT)² × (A × L).

Given: Y = 10¹² dynes/cm², α = 10^-6/°C, ΔT = 100°C, A = 10 cm², L = 100 cm.

Plugging in the values:

$E=\frac{1}{2}\times {10}^{12}\times {({10}^{-6}\times 100)}^2\times (10\times 100)$

$E=\frac{1}{2}\times {10}^{12}\times {\left({10}^{-4}\right)}^2\times {10}^3=\frac{1}{2}\times {10}^{12}\times {10}^{-8}\times {10}^3=\frac{1}{2}\times {10}^7$

E = 0.5 × 10⁷ erg = 5 × 10⁶ erg. Since 1 J = 10⁷ erg, E = 0.5 J = 500,000 μJ. This value is not among the small options, suggesting a miscalculation. Re-evaluating the exponent: 12 + (-8) + 3 = 7, so 10⁷ erg = 1 J. The provided small options (μJ) imply the intended calculation might be for energy in μJ directly from the formula, or there is a unit oversight. The calculation yields 500,000 μJ, which is not listed, so the correct answer is likely "None".

Final Answer: None