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An external pressure P is applied on a cube at 0 °C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by

Asked in JEE Main 2017 · Thermal stress and strain

• (1) P/(3α K)
• (2) P/(α K)
• (3) (3α)/(PK)
• (4) 3PKα

Step-by-step solution

Why the other options are wrong

• (2) comes from uses the linear coefficient α where the volume coefficient 3α belongs. The pressure changes a volume, so the expansion that undoes it must be a volume expansion.
• (3) comes from is the reciprocal of the key up to the factor 3, and it fails the simplest check: a bigger pressure should need more heating, but here Δ T falls as P rises.
• (4) comes from multiplies where the balance divides. Again a stiffer material — larger K — is harder to squeeze and so needs *less* heating to restore, yet this expression grows with K.

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