Question

The pressure applied on a cube from all sides is \(P\). In order to keep its volume constant, the temperature of the cube is to be raised by (The bulk modulus and the coefficient of volume expansion of the material of the cube are \(\beta\) and \(\alpha\) respectively)

• A. \(\dfrac{P}{\alpha\beta}\)
• B. \(\dfrac{P\alpha}{\beta}\)
• C. \(\dfrac{P\beta}{\alpha}\)
• D. \(\dfrac{\alpha\beta}{P}\)

Hint:

Remember: \[ \frac{\Delta V}{V} = -\frac{P}{\beta} \] for compression under pressure, and \[ \frac{\Delta V}{V} = \alpha\Delta T \] for thermal expansion. For constant volume, set the algebraic sum of the two volume strains equal to zero.

Answer 1

The Correct Option is A

Concept: Net volume strain = \(\alpha\Delta T - P/\beta = 0 \Rightarrow \Delta T = P/(\alpha\beta)\).

Step 1: Write the final answer. \(\boxed{\Delta T=\frac{P}{\alpha\beta}}\)