Question

The pressure applied from all directions on a cube is $p$. How much its temperatures should be raised to maintain the original volume? The volume elasticity of the cube is $\beta$ and the coefficient of volume expansion is $\alpha$.

• A. $\frac{p}{\alpha \beta }$
• B. $\frac{p\alpha }{\beta }$
• C. $\frac{p\beta }{\alpha }$
• D. $\frac{\alpha \beta }{p}$

Answer 1

The correct option is A $\frac{p}{\alpha \beta }$

If coefficient of volume expansion is $\alpha$ and rise in temperature is

$\Delta \theta$, then $\Delta$V$=$V$\alpha \Delta \theta$

$\Rightarrow \frac{\Delta V}{V}=\alpha \Delta \theta$

$\therefore$ Volume elasticity, $\beta =\frac{\rho }{\Delta V/V}$

$=\frac{\rho }{\alpha \Delta \theta }$

$\Rightarrow \Delta \theta =\frac{\rho }{\alpha \beta }$.