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Mechanical Properties of Solids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMechanical Properties of Solids3 Marks
Question
A uniform pressure P is exerted on all sides of a solid cube. It is heated through tºC in order to bring its volume back to the value it had before the application of pressure. Find the value of t.
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Answer

Let $\gamma=$ coefficient of cubical expansion of the cube. Let K be bulk modulus of elasticity of its material. V = initial volume, P = pressure applied, $\Delta\text{V}=\text{Decrease in its volume}$ $\therefore$ By definition, $\text{K}=\frac{\text{P}}{\frac{\Delta\text{V}}{\text{V}}}\ \text{or }\Delta\text{V}=\frac{\text{PV}}{\text{K}}\ ...(\text{i})$ Also, $\Delta\text{V}\propto\text{V}$ $\propto\text{t}\ \text{or }\Delta\text{V}=\gamma\text{V}\times\text{t}=\gamma\text{V}\text{t}\ ...(\text{ii)}$ Where, = rise in its temperature so as to increase the volume by $\Delta\text{V}$ s.l. it is brought back to its initial volume. $\therefore$ From (i) and (ii), we get, $\frac{\text{PV}}{\text{K}}=\gamma\text{V}\text{t}\ \text{or}\ \text{t}=\frac{\text{PV}}{\text{K}\gamma\text{V}}=\frac{\text{P}}{\gamma\text{K}}.$

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