The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume ? The volume elasticity of the cube is $β$ and the coefficient of volume expansion is $α$

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Solution

The correct option is A
Change in volume due to rise in temperature $Δ V = V α Δ θ$
$∴$ volumetric strain = $\frac{Δ V}{V}$ = $α Δ θ$
But bulk modulus $\Rightarrow$ $β$ = $\frac{s t r e s s}{s t r a i n}$ = $\frac{P}{α Δ θ}$ $∴$ $θ$ = $\frac{P}{α β}$

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The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume ? The volume elasticity of the cube is β and the coefficient of volume expansion is α

The correct option is A Change in volume due to rise in temperature ΔV=VαΔθ ∴ volumetric strain = ΔVV = αΔθ But bulk modulus ⇒ β = stressstrain = PαΔθ ∴ θ = Pαβ

The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume ? The volume elasticity of the cube is $β$ and the coefficient of volume expansion is $α$

The correct option is A
Change in volume due to rise in temperature $Δ V = V α Δ θ$
$∴$ volumetric strain = $\frac{Δ V}{V}$ = $α Δ θ$
But bulk modulus $\Rightarrow$ $β$ = $\frac{s t r e s s}{s t r a i n}$ = $\frac{P}{α Δ θ}$ $∴$ $θ$ = $\frac{P}{α β}$