A rubber of volume 2000 cc is alternately subjected to tension and released. The figure shows the stress-strain curve of rubber. Each curve is a quadrant of an ellipse. The amount of energy lost as heat per cycle per unit volume will be

Hysteresis loss corresponding to elasticity per unit volume of a substance is given by the area of hysteresis loop, i.e., stress-strain curve coresponding to one complete loading and deloading.

Area of an ellipse = $\mathrm{\pi }$ x semi-majoraxis x semi-minor axis

${\mathrm{A}}_1 = \frac{1}{4}(\mathrm{\pi }\times 8\times 4\times {10}^2) \mathrm{and} {\mathrm{A}}_2 = \frac{1}{4}(\mathrm{\pi }\times 8\times 4\times {10}^2)$

Also, ${\mathrm{A}}_3 = 8\times 4\times {10}^2$

Area by hysteresis loop is A = ${\mathrm{A}}_1+{\mathrm{A}}_2-{\mathrm{A}}_3$

$\mathrm{A} = 2[\frac{\mathrm{\pi }}{4}\times 8\times 4\times {10}^2]-[8\times 4\times {10}^2]$

    = work done per cycle

    = energy lost per cycle per unit volume