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Q.

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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a

$\frac{αβ}{P}$

b

$\frac{Pα}{β}$

c

$\frac{P}{αβ}$

d

$\frac{Pβ}{α}$

answer is A.

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Detailed Solution

If coefficient of volume expansion is $α$ and rise in temperature is $∆ θ then ∆ V = Vα ∆ θ \Rightarrow \frac{∆ V}{V} = α ∆ θ$

Volume elasticity $β = \frac{P}{\frac{∆ V}{V}} = \frac{P}{α ∆ θ} \Rightarrow ∆ θ = \frac{P}{αβ}$

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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